Question

Imani has two part time jobs, one that pays $7.50 per hour for dog grooming at a pet store and another that pays $8.25 per hour at a grocery store. The number hours that she works varies from one week to another, depending on the demand from each job. Help her find a way to earn $500 dollars over a 4-week period.

A- Write expressions that shows the amount of money Imani earns at each at job. then construct a model that shows how she can earn$500.

Answer 1

Imani's income model incorporates hourly rates for dog grooming and grocery store jobs over a 4-week period. By summing earnings for each week, the equation T = $500 allows tracking progress toward her $500 income goal.

Earning Expressions and Model for Imani's Income

Expressions for Hourly Earnings:

Dog Grooming:

Let dg represent the number of hours worked at the dog grooming job.

Earning Expression: dg * $7.50

Grocery Store:

Let gs represent the number of hours worked at the grocery store job.

Earning Expression: gs * $8.25

Model for Total Income over 4 Weeks:

Total Income:

Let T represent Imani's total income over the 4-week period.

Expression: T = dg1 * $7.50 + gs1 * $8.25 + dg2 * $7.50 + gs2 * $8.25 + dg3 * $7.50 + gs3 * $8.25 + dg4 * $7.50 + gs4 * $8.25

4-Week Income Goal:

Imani wants to earn $500.

Constraint: T = $500

This model allows you to plug in the number of hours Imani works at each job in each week (dg1, gs1, dg2, gs2, etc.) and then solve for the total income (T) to see if she reaches her goal of $500.

Example Scenario:

If Imani works 8 hours at the dog grooming job and 12 hours at the grocery store in week 1, her income for that week would be:

(8 * $7.50) + (12 * $8.25) = $60 + $99 = $159