Exam 3: Simple Equations and Word Problems

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

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

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?

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?

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

Find three consecutive integers whose product is -60 .

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

A horizontal bar of negligible weight has an $82.6 \mathrm{~kg}$ weight hanging from the left end and a $43.0 \mathrm{~kg}$ weight hanging from the right end. The bar is seen to balance $56.2 \mathrm{~cm}$ from the right end. Determine the length of the bar.

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

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

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 $\$ 46,458$ ?

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?

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 $105 \mathrm{~km} / \mathrm{h}$ ?

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.

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

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

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

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

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 $\$ 23,617$ ?

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