David bought 4 pairs of shoes and 2 T-shirts for $980. If 1 pair of shoes cost the same as 2 T-shirts, what is the cost of 1 pair of shoes and 1 T-shirt?
Question
David bought 4 pairs of shoes and 2 T-shirts for $980. If 1 pair of shoes cost the same as 2 T-shirts, what is the cost of 1 pair of shoes and 1 T-shirt?
Solution
Let's denote the cost of one pair of shoes as S and the cost of one T-shirt as T.
From the problem, we know that David bought 4 pairs of shoes and 2 T-shirts for $980. So, we can write this as an equation:
4S + 2T = 980
We also know from the problem that one pair of shoes costs the same as two T-shirts. So, we can write this as another equation:
S = 2T
Now we can solve these equations step by step.
First, substitute S from the second equation into the first equation:
4(2T) + 2T = 980 8T + 2T = 980 10T = 980
Now, solve for T:
T = 980 / 10 T = 98
Now that we know the cost of one T-shirt, we can find the cost of one pair of shoes by substituting T into the second equation:
S = 2T S = 2(98) S = 196
So, one pair of shoes costs 98.
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