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 180 o. For the triangle below, write and solve an equation to find the measure of the missing angle. 35 o 45 o xoxo Let x = the measure of the missing angle x = 180 The sum of the angles is x = x = 100 The measure of the missing angle is

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. There are 7 days in a week. 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 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)= $ w = $45 3 w = $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 = 2w 2 8 cm = w The width of the rectangle is 8 cm. 16 cm w w 48 = 2(16) + 2w 48 = w

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 = c = c = 4 2 c = $2 Each lemonade costs $2.