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Question

Louis and Mary went shopping and spent the same amount of money. Mary bought 4 equally priced notebooks and a pen that cost $3. She also bought a paperback that cost as much as 3 of the notebooks. Louis bought one of the same notebooks as Mary and spent another $21 on shoes. How much money did each person spend?

Answer 1

Step 1) Define variables

n = notebook

b = paperback = 3n

p = pen = 3

Since 1 paperback (b) costs the same as 3 notebooks (n), we can write:

b = 3n

Step 2) Define equation for Mary's total

Adding all the items we get:

Total = 4n + 3 + 3n 

Combine like terms

Total = 7n + 3

Step 3) Define equation for Louis's total

Total = n + $21

Step 4) Set the equations equal to each other, then solve for n.

Since Mary and Louis spent the same amount of money, we can set the two equations equal to one another. Therefore:

7n + 3 = n + 21

->Subtract n from both sides

6n + 3 = 21

->Subtract 3 from both sides 

6n = 18 

->Divide both sides by 6

n = 3 

Step 5) Plug n = 3 into each person's equation to find their total.

Recall Mary spent a total of 7n + 3. Substitute 3 in for n. 

Total = 7(3) + 3

Total = 21 + 3 

Total = $24

Recall Louis spent a total of n + 21. Substitute 3 in for n. 

Total = 3 + 21 

Total = $24 

Each person spent $24. As stated, their total spent was the same.