quan is shopping. he can buy 2 pants and 1 shirt for $79.85 (before tax is added). he can but 1 pair of pants and 2 shirts for $69.85 (before tax is added). how much does a shirt cost?
a)$29.95
b)$10.50
c)$19.95
d)$5.50
and the answer that i picked is b
thanks
To find out how much a shirt costs, we can use algebraic reasoning by assuming the cost of a pair of pants as 'p' and the cost of a shirt as 's'.
From the information given, we can create two equations:
Equation 1: 2p + s = 79.85 (equation representing the cost of 2 pants + 1 shirt)
Equation 2: p + 2s = 69.85 (equation representing the cost of 1 pant + 2 shirts)
To find the cost of a shirt, we need to solve the system of equations above. Here's one way to do it:
Step 1: Rearrange Equation 1 to solve for s:
s = 79.85 - 2p
Step 2: Substitute the value of s from Step 1 into Equation 2:
p + 2(79.85 - 2p) = 69.85
Step 3: Simplify the equation:
p + 159.7 - 4p = 69.85
Step 4: Combine like terms:
-3p + 159.7 = 69.85
Step 5: Move constants to one side and variables to the other:
-3p = 69.85 - 159.7
-3p = -89.85
Step 6: Solve for p:
p = -89.85 / -3
p ≈ 29.95
Step 7: Substitute the value of p into Equation 1 or 2 to find the value of s. Using Equation 1:
2(29.95) + s = 79.85
59.90 + s = 79.85
s = 79.85 - 59.90
s ≈ 19.95
Therefore, the cost of a shirt is approximately $19.95. So, the correct answer is option c) $19.95, not b) $10.50.