Exam 3: Simple Equations and Word Problems

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

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 $28.0 \%$ ?

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?

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

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

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?

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?

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?

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

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

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 $540 \mathrm{~kg}$ .

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

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

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

Find three consecutive integers whose sum is 81 .

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

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

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?

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?

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