Math Problem Statement

$2,100 is shared between Jennifer and Justin. Justin's share is $40 more than Jennifer's share. a. What is Jennifer's share?

Round to the nearest cent b. What is Justin's share?

Solution

Let's define Jennifer's share as xx dollars. Since Justin's share is $40 more than Jennifer's, Justin's share will be x+40x + 40.

The total amount shared between them is $2,100, so we can set up the following equation:

x+(x+40)=2,100x + (x + 40) = 2,100

Simplifying the equation:

2x+40=2,1002x + 40 = 2,100

Subtract 40 from both sides:

2x=2,0602x = 2,060

Now, divide by 2:

x=1,030x = 1,030

a. Jennifer's share is $1,030.00.

b. To find Justin's share:

x+40=1,030+40=1,070x + 40 = 1,030 + 40 = 1,070

Justin's share is $1,070.00.

Let me know if you'd like more details or have questions. Here are 5 related questions to expand on this:

  1. How would the shares change if Justin's share was $60 more than Jennifer's?
  2. What if the total amount shared was $3,000, with the same $40 difference?
  3. What if Jennifer's share was $50 more than Justin's instead?
  4. How would you set up the equation if the total was $2,100, but Justin got double Jennifer's share?
  5. What if the total amount shared was split evenly between the two?

Tip: Always define variables clearly when solving word problems involving shared amounts to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Word Problems

Formulas

x + (x + 40) = 2100
2x + 40 = 2100

Theorems

Basic Linear Equation Solving

Suitable Grade Level

Grades 6-8