Exam 3: Simple Equations and Word Problems

Two consecutive integers add to 199. What are they?

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?

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?

A $2.75 \mathrm{~m}$ horizontal bar of negligible weight hangs from two cables, one at each end. When a downward force of $215 \mathrm{~N}$ is applied to the bar, the tension in the left cable is $275 \mathrm{~N}$ . How far from the right cable was the force applied?

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?

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?

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

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

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

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

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?

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

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?

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

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

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

A $6.50 \mathrm{~m}$ horizontal bar of negligible weight hangs from two cables, one at each end. When a downward force is applied to the bar, the tension in the left cable is $124 \mathrm{~N}$ and the tension in the right cable is 235 N. How far from the right cable was the force applied?

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

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

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