Math Problem Statement

Gabe goes to the mall. If k is the number of items he bought, the expression 12k + 27 gives the amount he spent in dollars at one store. Then he spent 28 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 7 items.

Solution

Let's break down the problem step-by-step.

  1. Given Expression: The expression provided is 12k+2712k + 27, which represents the amount Gabe spent in dollars at one store. Here, kk is the number of items Gabe bought.

  2. Additional Spending: Gabe also spent an additional 28 dollars at another store.

  3. Total Spending: To find the total amount Gabe spent at the mall, we need to add these two amounts together.

Solution

The expression for Gabe's total spending at the mall can be written as: 12k+27+2812k + 27 + 28

Simplifying this expression by adding the constants (27 and 28): 12k+5512k + 55

So, the expression that represents the total amount Gabe spent at the mall is: 12k+5512k + 55

Estimating for k=7k = 7

If Gabe bought 7 items, substitute k=7k = 7 into the expression: 12(7)+55=84+55=13912(7) + 55 = 84 + 55 = 139

Therefore, Gabe would have spent 139 dollars if he bought 7 items.

Would you like further details on this solution, or do you have any questions?


Related Questions:

  1. What if Gabe bought 10 items? How much would he spend?
  2. How would the expression change if the first store used a different formula for spending, like 10k+2510k + 25?
  3. If Gabe spent 15 dollars at the second store instead of 28, what would the new total expression be?
  4. What would the total amount be if Gabe bought no items (k=0k = 0)?
  5. How much more would Gabe spend if each item at the first store cost 15 dollars instead of 12?

Tip:

When dealing with expressions, remember to combine like terms (constants with constants, terms with kk with other terms with kk) for simpler expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Expression Simplification

Formulas

12k + 27 + 28
12k + 55

Theorems

-

Suitable Grade Level

Grades 6-8