What is the property that justifies the illustrated step in solving the equation?
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Answers:
one t-shirt costs $10
one pair of shorts costs $15
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Explanation:
x = cost of one t-shirt
y = cost of one pair of shorts
13x+17y = 385 is the first equation because 13x represents the money you get from selling 13 shirts, and the 17y represents the amount you get from selling 17 shorts. The total 13x+17y is given to be $385
The second equation is 13x+12y = 310 for similar reasoning, but this time you sell 12 shorts this time and you get $310 in revenue.
The system of equations we have is:
There are a few ways to solve this system. Possibly the quickest method is to note that the 13x shows up twice, so we can subtract straight down to eliminate the x terms
So,
- 13x-13x becomes 0x or just 0, and the x terms go away.
- 17y-12y becomes 5y
- 385-310 becomes 75
After those three subtractions, we have the equation 5y = 75 which solves to y = 15 after dividing both sides by 5. This means the cost of one pair of shorts is $15
Plug this y value into any equation involving x and y, and solve for x
13x+17y = 385
13x+17(15) = 385
13x+255 = 385
13x = 385-255
13x = 130
x = 130/13
x = 10
Therefore, each t-shirt costs $10
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To help verify the answer, plug (x,y) = (10,15) into each equation. We should end up with a true result after simplifying both sides.
Start with the first equation
13x+17y = 385
13(10)+17(15) = 385
130+255 = 385
385 = 385
We get a true result which confirms the first equation.
Repeat for the second equation.
13x+12y = 310
13(10)+12(15) = 310
130+180 = 310
310 = 310
Both equations are true so (x,y) = (10, 15) has been fully confirmed.