Writing Two-Step Equations

Equation – a mathematical sentence containing variables, numbers and

operation symbols

Two-step equation – an equation with a combination of:

multiplication or division

with

addition or subtraction

Keywords

• Is, was: equal• Increased by: +• More than: +

• Decreased by: -• Less: -• Less than: -

• The product of: • ( )• Twice: • 2• Triple: • 3

• The quotient of: ÷

The product of a number and four increased by seven is thirty-one.

4x + 7 = 31

+ -7 + -7

4x = 24

4 4

x = 6

Mrs. Copple’s father is 71 years old. This is thirty-one less than six times

Mrs. Copple’s son’s age.

Find my son’s age.

6a – 31 = 71

+31 +31

6a = 102

6 6

a = 17

The quotient of a number and negative five less twelve is negative one.

n - 12 = -1

-5

+ 12 +12

(-5) • n = 11 • (-5)

-5

n = -55

Nineteen less than a number divided by two is thirty.

x - 19 = 30

2

+19 +19

2 • x = 49 • 2

2

x = 98

Jill earns $8 an hour forbabysitting plus a $5 tip.Last night Jill earned $37.How many hours did shebabysit?

8h + 5 = 37 -5 -5 8h = 32 8 8 h = 4

Sam had a certain numberof baseball cards (c). Hesplit then evenly among

histwo brothers. Sam’s friend gave him 15 more for his birthday. If Samwould have had 65 cardsafter his friend gave himsome, before splitting them among his brothers,how many cards did Samhave in the beginning? c + 15 = 65 2

331 students went on afield trip. Six buses

werefilled and 7 studentstraveled in cars. Howmany students were oneach bus? 6b + 7 = 331 - 7 - 7 6b = 324 6 6 b = 54

Alice had $24 to spend on

seven pencils. Afterbuying them, she had

$10.How much did each

pencilcost? 7p + 10 = 24 - 10 - 10 7p = 14 7 7 p = 2

Maria bought seven boxes.

A week later, half of all ofher boxes were destroyedin a fire. There are now22 boxes left. How manydid she have in thebeginning?

b + 7 = 22 2 - 7 - 7 b = 15 2 b = 30

Ian spent half his weeklyallowance playing mini-

golf.To earn more money, hisparents let him wash thecar for $4. What is hisweekly allowance if he ended with $12? a + 4 = 12 2 - 4 - 4 a = 8 2 a = 16

How old an I if 400 reduced by 2 times my

ageis 244?

400 – 2a = 244 400 + (-2a) = 244 - 400 - 400 -2a = -156 -2 - 2 a = 78

The Cooking Club made some pies to sell at a basketball

gameto raise money. The cafeteriacontributed four pies to the sale. Each pie was then cutinto five pieces and sold. Therewere a total of 60 pieces tosell. How many pies did the

clubmake? p + 20 = 60 5 - 20 - 20 p = 40 5 p = 200

Joe’s father is 45. He is15 years older than

twiceJoe’s age. How old is

Joe?

2j + 15 = 45 - 15 - 15 2j = 30 2 2 j = 15

Your mother took you shopping this weekend. She purchased jeans andshirts. The jeans cost$45 each and the shirtscost $25 each. If shebought twice as manyshirts as jeans, and spent$190 on you, how manyjeans and how many

shirtsdid she buy? 45j + 2(25j) = 190 45j + 50j = 190 jeans = 2 shirts = 4

On a prealgebra test, thehighest grade was 42 points higher than thelowest grade. The sum

ofthe two grades was 138.What was the lowestgrade? g + g + 42 = 138 2g + 42 = 138 - 42 - 42 2g = 98 2 2 g = 49

Jamie drove twice as faras Rhonda. Together,

theydrove 90 miles. Find thenumber of miles driven

by each girl.

Let ‘m’ stand for Jamie’smiles. Let ‘2m’ stand forRhonda’s miles.

m + 2m = 90 3m = 90 3 3 m = 30

The length of a rectangular map

is 15 inches. The perimeter of

the map is 50 inches. Find the

width.

P = l + w + l + w P = 2(l + w)

50 = 2(15 + w) 50 = 30 + 2w -30 -30 20 = 2w 2 2 10 = w

Jose has a board that is 44 inches long. He wants to cut itinto two pieces so that one piece is six inches longer thanthe other. How long should theshorter piece be?

Let ‘p’ be the shorter piece. Let ‘p + 6’ be the longer piece.

p + p + 6 = 44 2p + 6 = 44 - 6 - 6 2p = 38 2 2 p = 19 shorter = 19” longer = 25”