Basic Math Skills - Applications of Linear Equations

Vocabulary

100

Sum

Addition

200

Less than

Subtract

300

Product

Multiply

400

Quotient

Divide

500

Double

Multiply by 2

Translating Expressions

100

the sum of a quantity and two

x + 2

200

The quotient of a number and ten

x / 10

300

five from twice a number

2x - 5

400

the quotient of three times a number and five

3x / 5

500

ten less than half of a number

1/2 x - 10 or .5x - 10

Writing Equations

100

Emily and Janet are selling tickets for the game.  Each ticket costs $5, and they also received $18 in donations.  If they collected $123, then how many tickets did they sell?

Write the equation to solve this problem.

5x + 18 = 123

200

Emanuel is comparing gym memberships.  For the first gym, the one-time sign on fee is $50 with a monthly price of $20.  For the second gym, the one-time sign on fee is $0 but the monthly price is $30.  When would the total costs of the two memberships be the same?

Write an equation for this situation.

20x + 50 = 30x

300

The width of a rectangle is five more than the length.  If the perimeter of the figure is 18 cm, then what are the dimensions?

Write an equation to model this situation.

x + x + 5 + x + x + 5 = 18

or 4x + 10 = 18

400

Marcus is laying down carpet in his living room.  He has order 200 ft² of carpet.  He knows that the length of his living room is twice as long as the width.  What are the dimensions of his living room?

Write an equation to represent this situation.

x(2x) = 200

or 2x² = 200

500

The first side of a triangle is 3 cm shorter than the second side.  The third side is 4 times as long as the first side.  The perimeter is 27 cm.  Find the length of each side.

Write an equation to represent this situation.

x + x - 3 + 4(x - 3) = 27

or 6x - 15 = 27

Area and Perimeter

100

Find the perimeter of a square with each side length of 3 cm

12 cm

200

Find the area of a rectangle with side lengths 5 cm and 8 cm

40 cm²

300

Find the perimeter of a rectangle with side lengths of 5 cm and 7 cm

24 cm

400

Find the perimeter of a triangle with side lengths 5 in, 4 in, and 8 in.  

17 inches

500

Find the area of a triangle that has a base of 10 inches and a height of 4 inches.

20 inches²

Word Problems

100

Emily and Janet are selling tickets for the game.  Each ticket costs $5, and they also received $18 in donations.  If they collected $123, then how many tickets did they sell?

Solve 5x + 18 = 123

They sold 21 tickets

200

Emanuel is comparing gym memberships.  For the first gym, the one-time sign on fee is $50 with a monthly price of $20.  For the second gym, the one-time sign on fee is $0 but the monthly price is $30.  When would the total costs of the two memberships be the same?

the costs would be the same after 5 months.

300

The width of a rectangle is five more than the length.  If the perimeter of the figure is 18 cm, then what are the dimensions?

The length is 2 cm

The width is 7 cm

400

Marcus is laying down carpet in his living room.  He has order 200 ft² of carpet.  He knows that the length of his living room is twice as long as the width.  What are the dimensions of his living room?

Solve 2x² = 200

length is 20 ft, width is 10 ft.

500

The first side of a triangle is 3 cm shorter than the second side.  The third side is 4 times as long as the first side.  The perimeter is 27 cm.  Find the length of each side.

Solve 6x - 15 = 27

First side is 4 cm

Second side is 7 cm

Third side is 16 cm