Writing and solving equations from story problems

Some things to remember when solving story problems:

• Read the question carefully.

• Define the variable.

• Write an equation.

– A verbal model or a diagram often helps!

• Solve and check the equation.

• Answer in a complete sentence.

Ex. 1) The sum of the measures of the angles of a triangle is 180o. For the triangle below, write and solve an equation to find the measure of the missing angle.

35o 45o

xo

Let x = the measure of the missing angle

35 + 45 + x = 180 The sum of the angles is 1800.

80 + x = 180- 80 - 80

x = 100The measure of the missing angle is 1000.

Ex. 2) Sam sent 574 text messages last week. On average, how many messages

did he send each day? Write and solve an equation to find the answer.

Let x = the number of messages sent each day

A verbal model may help you write the equation.

dayper messagesdays total

messages total

xdays 7

messages 574 There are 7 days in a week.

xdayeach messages 28 Sam sent an average of 82 messages each day.

Ex. 3) A race car can travel at a rate of 205 miles per hour. At this rate, how

far would it travel in 3 hours? Write and solve an equation to find the answer.

Let d = distance traveled

We can use the distance formula distance = rate (time) to find out how

far the car traveled.

d = (205 miles per hour )( 3 hours)

d = 615 miles

The race car traveled 615 miles.

Ex. 4) Three fourths of the students in Mr. Miller’s homeroom brought in their permission slips for the field trip. If 18 students brought in their slips, how many total students are in Mr. Miller’s homeroom? Write and solve

an equation to find the answer.

Let n = the number of students in homeroom

students 18class theof 4

3

184

3n

3

4

3

4

students 24 n There are 24 students in Mr. Miller’s homeroom.

Ex. 5) Ryan is saving money for a skateboard that costs $85. He already has $40, and he plans to save the rest of the money over the

next 3 weeks. How much will he need to save each week to have enough for the skateboard?

Write and solve an equation to find the answer.

Let w = average weekly savings

Verbal model: money Ryan has + money he’ll save = $85

$40 + 3w = $85

money Ryan has + (3 weeks)(money per week)= $85

- 40 - 40

3w = $453 3w = $15

Ryan needs to save $15 each week.

Ex. 6) The perimeter of a rectangle is 48 centimeters. Its length is 16 centimeters. What

is the width of the rectangle? Write and solve an equation to find the answer.

Let w = width of the rectangle

The perimeter is the distance around the outside of the rectangle.

P = 2L + 2w

- 32 -3216 = 2w

2 2

8 cm = w

The width of the rectangle is 8 cm.

16 cm

16 cm

w w

48 = 2(16) + 2w48 = 32 + 2w

Ex. 7) Vinny and his brother bought 2 hamburgers and 2 lemonades. The hamburgers cost $6 each. They spent a total

of $16. How much did each lemonade cost? Write and solve an equation to find the answer.

Let c = cost of one lemonade

Verbal model: cost of 2 burgers + cost of 2 lemonades = $16

2(6) + 2c = 16 12 + 2c = 16- 12 -12

2c = 42 2

c = $2Each lemonade

costs $2.