7.EE-Solve multi-step real-life and mathematical problems

Algebra:

CCSS.MATH.CONTENT.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Problem:

Joe works at a concessions stand at Century Link Field. Joe makes $10 per hour plus any tips he gets from the generous football fans. Set up and solve an equation for EACH of the given problems and write your answer using complete sentences.

1. Set up a general equation for the total amount of money Joe will earn working at the concessions stand. Define your variables.
2. How much money does Joe make if he works 4 hours and makes $17 in tips?
3. If Joe makes $86 dollars total, and earned $31 dollars in tips, how many hours did he work?
4. Joe worked with Steve during the Seahawk v. 49ers game. They worked 6 hours and made $46 in tips together. If Steve and Joe split the tips evenly, how much money did Joe make during that game?

Commentary:

The purpose of this problem is to illustrate the Common Core State Standard of applying a real-world situation to learning how to set up and solve single variable equations. The students learned how to manipulate one and multi-step equations. Teachers can use this problem as a summative assessment. This problem gives them the chance to reason how to set up an equation using information that is provided for them. Students are able to define variables for an equation and use values to evaluate for the unknown variables. The students use the additive and multiplicative inverses to further their mathematical understanding of solving equations. The students will get a chance to change an equation so that it fits what a question is asking. For example, changing the original equation from T=10x+y to T=10x+(y/2) to factor in the tips being split. The story problem has multiple parts, so this gives the students the opportunity to read and follow directions carefully.

Solution:

1. Let x be the number of hours that Joe worked, let y be the number of tips in dollars, and let T be the total number Joe earned in dollars. The student can pick any variable for the given information but the equation must be set up in the correct order. The number of hours worked must be multiplied by the wage, so 10x. Then the tips will be added to that making the entire equation T=10x+y.

x= number of hours worked

y= number of tips earned in dollars

T= total number dollars earned

T=10x+y

2. The number of tips, $17, should be plugged into y for the given equation.

T=10x+17

Then since we know that Joe worked for 4 hours, we can evaluate when x=4.

T=10(4)+17

T=40+17

T=57

            Joe earned $57 total.

3. The total number of money that Joe earned was $86 dollars and his tips were $31. For the equation the students must evaluate when T = 86 and y = 31. Then the students must solve the equation for x.

86=10x+31

55=10x

5.5=x

Joe worked for 5 and a half hours.

4. Since the amount of tips earned were shared by 2 people, the total number of tips needs to be divided by 2 to find Joe’s share.

T=10x+(y/2)

            Then evaluate the equation when x = 6 and y = 46.

T=10(6)+((46)/2)

T=60+23

T=83

            Joe earned $83 total.