Writing and solving equations from story problems
What’s the Problem?!?
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.
32o
97o
xo
Let x = the measure of the missing angle
32 + 97 + x = 180 The sum of the angles is 1800.
129 + x = 180- 129 - 129
x = 51The measure of the missing angle is 510.
Ex. 2) Last week, Sam sent 798 text messages . 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 798 There are 7 days in a week.
xdayeach messages 141 Sam sent an average of 114 messages each day.
Ex. 3) A race car can travel at a rate of 197 miles per hour. At this rate, how far would it travel in 2.5 hours? Round your
answer to the nearest mile.
Let d = distance traveled
We can use the distance formula distance = rate (time) to find out how
far the car traveled.
d = (197 miles per hour )( 2.5 hours)
d = 492.5 miles
The race car traveled about 493 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 43
1843
n
34
34
students 24 n There are 24 students in Mr. Miller’s homeroom.
Ex. 5) Eric is saving money for a snowboard that costs $215. He already has $119, and he plans to save the rest of the money over the next 4 weeks. How much will he need to save each week to
have enough for the snowboard?
Let w = average weekly savings
Verbal model: money Eric has + money he’ll save = $215
$119 + 4w = $215
money Eric has + (4 weeks)(money per week)= $215
- 119 - 119
4w = $964 4w = $24
Eric needs to save $24 each week.
Ex. 6) The perimeter of a rectangle is 62 inches. Its width is 9 inches. What is the
length of the rectangle?
Let L = length of the rectangle
The perimeter is the distance around the outside of the rectangle.
P = 2L + 2w
- 18 -1844 = 2L2 2
22 in = L The length of the rectangle is 22 inches.
9 in 9 in
L
L62 = 2L + 2(9)62 = 2L + 18
Ex. 7) Vinny and his Dad bought 2 sandwiches and 2 lemonades. The sandwiches cost $6.50 each. They spent a
total of $18. How much did each lemonade cost?
Let c = cost of one lemonade
Verbal model: cost of 2 sandwiches + cost of 2 lemonades = $18
2(6.50) + 2c = 18 13 + 2c = 18- 13 -13
2c = 52 2
c = $2.50Each lemonade
costs $2.50.
