Question

Pablo wants to spend $100 on clothing and he wants to purchase 6 additional clothing pieces for his wardrobe. Each pair of pants costs $20 and each shirt costs $15.

Part A. Identify the system of equation that represents this situation.

Part B. Determine if Pablo can buy 2 pair of pants and 4 shirts? Explain your answer.

Answer 1

A.
`x+y=6...(1)`

`20x+15y=100...(2)`

B. Yes, Pablo can buy 2 pair of pants and 4 shirts.

Explanation:

A. Let x be the number of pairs of pants and y be the number of shirts.

We have been given that Pablo wants to purchase 6 additional clothing pieces for his wardrobe. We can represent this information as:

`x+y=6...(1)`

We are also told that each pair of pants costs $20 and each shirt costs $15. So the cost of x pairs of pants will be 20x and cost of y shirts will be 15y.

As Pablo wants to spend $100 on clothing, so we can represent this information as:

`20x+15y=100...(2)`

Therefore, the system of equation representing the given situation will be:

`x+y=6...(1)`

`20x+15y=100...(2)`

B. To find if Pablo can buy 2 pair of pants and 4 shirts we will substitute x=2 and y=4 in our both equations.

`2+4=6`

`6=6`

`20*2+15*4=100`

`40+60=100`

`100=100`

We can see that x=2 and y=4 satisfies our both equation, therefore, Pablo can buy 2 pair of pants and 4 shirts.