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Eric and Jaren go shopping and they both buy new shoes and hats. Eric buys 2 pairs of shoes and 3 hats and his bill is $175. Jaren buys 4 pairs of shoes and only 1 hat and his bill is $225. What is the cost of one pair of shoes? What is the cost of one hat?

 Dec 3, 2020

Best Answer 

 #1
avatar+339 
+2

I think the latex screwed up there. I don't think you intended that to happen. But at least I can use latex normally now.

 

So let shoes be $s$ and hats be $h$. 

 

Eric: $2s+3h=175$

Jaden: $4s+1h=225$

 

Solve the system of equations.

 

We can set them similar to each other by multiplying Eric's by 2 and subtracting all of Jaden's from it.

 

$2\cdot(2s+3h=175)\\\implies4s+6h=350$

 

Cancel like terms:

 

4s+6h=350

-4s+1h=225

-------------------

5h=75

 

Now we have 5 hats are 75 dollars, so 1 hat is 15 Dollars.

 

Sub into the secone equation:

 

$4s+15=225$

$4s=210$

$s=52.5$

 

Thus a pair of shoes is 52.50 Dollars.

 Dec 4, 2020
 #1
avatar+339 
+2
Best Answer

I think the latex screwed up there. I don't think you intended that to happen. But at least I can use latex normally now.

 

So let shoes be $s$ and hats be $h$. 

 

Eric: $2s+3h=175$

Jaden: $4s+1h=225$

 

Solve the system of equations.

 

We can set them similar to each other by multiplying Eric's by 2 and subtracting all of Jaden's from it.

 

$2\cdot(2s+3h=175)\\\implies4s+6h=350$

 

Cancel like terms:

 

4s+6h=350

-4s+1h=225

-------------------

5h=75

 

Now we have 5 hats are 75 dollars, so 1 hat is 15 Dollars.

 

Sub into the secone equation:

 

$4s+15=225$

$4s=210$

$s=52.5$

 

Thus a pair of shoes is 52.50 Dollars.

Nacirema Dec 4, 2020

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