Deck 3: Simple Equations and Word Problems

Question 1

Solve and check this equation: $5 x+21=-2 x$

Answer 1

$x=-3$

Question 2

Solve and check this equation: $9-6 x+x=4$

Answer 2

$x=1$

Question 3

Solve and check this equation: $15 y=24+6 y$

Answer 3

$y=\frac{8}{3}$

Question 4

Solve and check this equation: $\frac{x}{4}=16$

Question 5

Solve and check this equation: $3 x+7-3 x=6-5 x$

Question 6

Solve and check this equation: $2(x+3)-4 x=2(11-2 x)$

Question 7

Solve and check this equation: $-3(4 x+1)=7-4 x$

Question 8

Solve and check this equation: $-2(-6+8 x)-4(1-2 x)=16$

Question 9

Solve and check this equation: $8-3 x(9-1)+6=-12(x-2)$

Question 10

Solve and check this equation: $6+12 x^{2}+2 x(3-6 x)+8=-2(3+2 x)$

Question 11

Solve and check this equation: $\frac{3 x}{2}+2 x-12=7 x+5$

Question 12

Solve and check this equation: $\frac{7 x-2}{5}=\frac{-8 x-4}{2}$

Question 13

Solve for $x: \frac{m-x}{x}=6 n(m+1)$

Question 14

Solve for $x: q(x+1)=\frac{x-p}{q}$

Question 15

Solve: $x+4=48$

Question 16

Solve for $x$ and check: $\frac{x}{4}+1=\frac{x}{5}$

Question 17

Solve: $8 a-5=11 a+10$

Question 18

Solve: $5(2 x-3)=6(4-4 x)+29$

Question 19

Solve for $x: 3(8-x)=11+y$

Question 20

Solve for $x: 7-2 x=a+3$

Question 21

Solve: $2 x^{2}+4 x+12=2 x^{2}-7 x+1$

Question 22

Solve: $x+(2 x+3)(x-2)=2(x-3)(x+4)$

Question 23

Solve: (x + 4)(4x + 7) = x² + (3x + 1)(x + 2)

Question 24

Solve and check this equation: $(x+3)(2 x-5)=2(x+1)(x+3)$

Question 25

Solve and check this equation. Treat the coefficients as approximate numbers, and round your answer accordingly: $3.75 x+4.55=1.70 x+1.23$

Question 26

Solve and check this equation. Treat the coefficients as approximate numbers, and round your answer accordingly: $4.5+8.2 x=9.4$

Question 27

Solve and check this equation. Treat the coefficients as approximate numbers, and round your answer accordingly: $17.50 x+12.00=9.45 x-10.00$

Question 28

Solve and check this equation: $5.0 x+8.6=3.0(x+4.0)$

Question 29

Solve for $R_{1}: R_{\mathrm{T}}=\frac{R_{1} R_{2}}{R_{1}+R_{2}}$

Question 30

Solve for $R_{1}: I_{T}=V\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right)$

Question 31

Solve and check this equation: $3 w-2(5 w+3)=-(6 w-1)$

Question 32

Two numbers add to 36 . One is $x$ . Write an algebraic expression for the other.

Question 33

Rewrite this statement as an algebraic expression: "the number of $\mathrm{kg}$ of sand in a cement mixture of $x$ $\mathrm{kg}$ that is $22 \%$ sand by weight"

Question 34

Rewrite this statement as one or more algebraic expressions with variable $x$ : " 4 consecutive even numbers"

Question 35

Rewrite this statement as an algebraic expression: "the distance travelled in 30 minutes by a train going $5 \mathrm{~km} / \mathrm{h}$ faster than the car driving at $x \mathrm{~km} / \mathrm{h}$ "

Question 36

Rewrite this statement as an equation: "The reciprocal of a number is equal to triple the number plus one"

Question 37

Rewrite this statement as one or more algebraic expressions with variable $x$ : the angles in a triangle, when one angle is three times another

Question 38

Rewrite this statement as an algebraic expression: "six more than twice a certain number"

Question 39

The circumference of a circle with radius $r$ is $2 \pi r$ . Write an algebraic expression for the radius of a circle with circumference $C$ .

Question 40

Rewrite this statement as an algebraic expression: "four times the sum of a number plus its reciprocal"

Question 41

Two consecutive integers add to 199. What are they?

Question 42

When a certain number is divided by 4 , the result is 11 less than 3 times the number. What is the number?

Question 43

Twice a number is 16 more than its value. What is the number?

Question 44

A number diminished by 3 is the same as 3 times one quarter of the number. What is the number?

Question 45

Find three consecutive integers whose sum is 81 .

Question 46

Find three consecutive integers whose product is -60 .

Question 47

Thirteen times a certain number is as much above 24 as three times the number is below 24 . Find the number.

Question 48

In a college with 18491 students, there are 1193 more science students than arts students. How many arts students are at the college?

Question 49

In a certain program there are three times as many first semester students as second semester students. The total enrollment for both semesters is 416 . How many students are enrolled in each semester?

Question 50

A company bought a car and a van for $\$ 66,500$ . The van cost 2.5 times more than the car. What did the van cost?

Question 51

The amount $y$ in an account paying simple interest is $y=a(1+n x)$ , where $a$ is the principal, $n$ is the interest rate, and $x$ is the number of years the principal has been invested. Solve this equation for the interest rate, $n$ .

Question 52

A student puts all of her summer earnings towards her $\$ 5,610$ tuition. She pays the remainder of the bill with a student loan at a simple interest rate of $5.00 \%$ . After one year she owes $\$ 1,250$ on the loan. How much did she earn from her summer job?

Question 53

A person invests part of $\$ 10,000$ at $4 \%$ and the remainder at $7 \%$ , simple interest. After one year, a total of $\$ 580$ in interest has been earned. How much is invested at each rate?

Question 54

A person sold a table and four identical chairs for $\$ 360$ , getting five times as much for the table as for each chair. What was the price of the table and of each chair?

Question 55

What salary should a person receive in order to take home $\$ 35,000$ after deducting $28 \%$ for taxes?

Question 56

A firm bid $\$ 16,820$ on a project. They must pay their team of technologists $\$ 449$ per hour and their other costs are $\$ 125$ per hour. If the firm expects to make a $19 \%$ profit, how many hours should the project take to complete?

Question 57

A bank requires a minimum $5 \%$ down payment for a mortgage. If a couple has $\$ 15,000$ saved, what is the maximum house price they can afford if they know they must hold back $\$ 2,500$ for closing costs?

Question 58

Senior designers working on a project earn $\$ 400$ per day while designers earn $\$ 300$ per day. How many of each are working if 10 are hired at a total cost of $\$ 3,300$ per day?

Question 59

Tax time! The tax rate is $23 \%$ but an extra $3 \%$ surtax is charged on any income over $\$ 45,000$ and no tax is charged on the first $\$ 7,900$ . How much tax is owed for an income of $\$ 46,458$ ?

Question 60

Ontarians pay a health tax premium based on their yearly taxable income. If taxable incomes up to $\$ 25,000$ pay a rate of $6.41 \%$ for the health tax premium, with no tax payable on the first $\$ 20,000$ , how much is the health tax premium for a taxable income of $\$ 23,617$ ?

Question 61

You bought a tablet at $40 \%$ off and paid $\$ 482.30$ , which includes $15 \% \mathrm{HST}$ . What was the original price?

Question 62

You can either pay $5.60 \%$ simple interest on a loan for one year, or pay a $\$ 35$ fee to reduce the rate to $4.90 \%$ . What is the least amount to borrow that would make the $\$ 35$ fee option a better choice?

Question 63

A field needs 2.3 tonnes of fertilizer. The plants cannot withstand more than $14 \%$ potash, but the only available fertilizer contains $29 \%$ potash. How much of this fertilizer must be diluted to make the required mixture?

Question 64

The law requires artificially-coloured drinks to contain no more than $5.0 \%$ of a certain dye. How much water must be added to a $2500 \mathrm{~L}$ vat of a beverage that contains $8.0 \%$ of the dye?

Question 65

A glass factory needs glass for beakers that are $95.5 \%$ silica and $4.50 \%$ boron. How much silica must be added to a mixture that is $10.1 \%$ boron and $89.9 \%$ silica to make a $105 \mathrm{~kg}$ supply of glass?

Question 66

How many kilograms of brass containing $58 \%$ copper must be melted with $1 \overline{0} 0 \mathrm{~kg}$ of brass containing $75 \%$ copper to produce a new brass containing $70 \%$ copper?

Question 67

How many litres of wine with $16.0 \%$ alcohol and how many litres of wine with $10.0 \%$ alcohol must be mixed together to make $80 \overline{0}$ liters of wine with $14.0 \%$ alcohol?

Question 68

Constantan is an alloy of $60 \%$ copper and $40 \%$ nickel used in resistors because of its temperature invariance. How much nickel must be added to $35.0 \mathrm{~kg}$ of copper to produce constantan?

Question 69

How much copper must be added to $8.0 \mathrm{~kg}$ of pure silver (usually $99.9 \%$ pure, but use $100 \%$ for your calculations) in order to make a sterling silver alloy of $92.5 \%$ silver and $7.5 \%$ copper?

Question 70

Gasoline containing $10.0 \%$ ethanol is to be boosted to $14.0 \%$ ethanol. How much ethanol must be added to $175 \mathrm{~L}$ to do this?

Question 71

How much pure sand must be added to $12.5 \mathrm{~kg}$ of cement mixture containing $23.0 \%$ sand to raise the sand content to $28.0 \%$ ?

Question 72

How many kilograms of cement containing $27.5 \%$ sand must be added to cement containing $20.0 \%$ sand to obtain $45.0 \mathrm{~kg}$ of cement that is $24.6 \%$ sand?

Question 73

The chemistry lab has $20 \%$ and $45 \%$ sulfuric acid solutions available. How much of each must be mixed to produce $875 \mathrm{~mL}$ of $32 \%$ solution needed for an experiment? Treat the percent amounts as exact numbers.

Question 74

A team of technicians can upgrade 17 laptops in one hour. The team starts to upgrade 150 computers, but after three hours the supervisor decides to add a second team. The second team can upgrade 4 machines every 20 minutes. How many hours and minutes does the entire job take?

Question 75

A $560 \mathrm{~km}$ road trip took 5.50 hours. The average speed for the first part was $95 \mathrm{~km} / \mathrm{h}$ . The speed limit changed and the last part was driven at an average speed of $105 \mathrm{~km} / \mathrm{h}$ . For how long was the speed $105 \mathrm{~km} / \mathrm{h}$ ?

Question 76

How many kilograms of cement containing $24.0 \%$ sand must be added to $45.0 \mathrm{~kg}$ of cement containing $19.0 \%$ sand to obtain cement that is $22.6 \%$ sand?

Question 77

A horizontal beam of negligible weight is $12.0 \mathrm{~m}$ long and is supported by columns at each end. A vertical load of $6500 \mathrm{~kg}$ is applied to the beam $x$ metres from the left end. Find $x$ so that the reaction at the left column is $3800 \mathrm{~kg}$ .

Question 78

A uniform horizontal beam weighing $136 \mathrm{~kg}$ is $10.4 \mathrm{~m}$ long and is supported by columns at each end. A vertical load of $1275 \mathrm{~kg}$ is applied to the beam $x$ metres from the right end. Find $x$ so that the reaction at the left column is $540 \mathrm{~kg}$ .

Question 79

A uniform horizontal beam weighing $215 \mathrm{~kg}$ is supported at each end by a column. A vertical load of $595 \mathrm{~kg}$ is placed $1.6 \mathrm{~m}$ from the left end. If the reaction at the left column is double the reaction at the right column, determine the length of the beam.

Question 80

A $3.75 \mathrm{~m}$ long horizontal beam of negligible weight is supported at each end by a column. When a vertical load is applied, the reaction at the left column is $124 \mathrm{~N}$ and the reaction at the right column is $617 \mathrm{~N}$ .
(a) What was the size of the vertical load?
(b) How far from the left end was the load applied?