Hello there! the answers to your question are:
a. $15x + $20y = $100; x + y = 6.
b. Yes, he can, since the cost of 4 shirts is $60, and two pants is $40, which adds up to be how much he is spending, or $100.
Let's start by working to solve part a. We need to set up a system of equations that models the situation given. To do this, let's set up an equation that models how many Sean will buy in total and how much he will spend.
The question says that he wants to spend $100 total, and shirts cost $15 and pants cost $20. We can model this as $15x + $20y = $100.
The question also says he wants to purchase a total of 6 items for his wardrobe, so the number of items he buys has to add up to 6. This can be modeled as x + y = 6.
This gives us our answer for part a. Now let's solve part b. We are being asked if Sean can buy 2 pants and 4 shirts. This fits one of our equations, x + y = 6, since 4 and 2 add up to be 6. We need to see if this fits our other equation, though $15x + $20y = $100. To do this, we can substitute the number of shirts (4) into the x value, and the number of pants (2) into the y value and solve. If the total is more than 100, he can't. If it is less, he can.
$15(4) + $20(2) = 100
60 + $20(2) = 100
60 + 40 = 100
Since our total adds up to $100, he can buy 2 pairs of pants and 4 shirts.
I hope this helps and have a great rest of your day!
