Exam 3: Simple Equations and Word Problems

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"

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.

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

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

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?

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

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?

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

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

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

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?

Solve: $x+4=48$

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, $n$ .

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 $x \mathrm{~km} / \mathrm{h}$ "

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?

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

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?

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?

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

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