ExplanationTo solve this problem, establish the following variables:
J = original jean price
B = original blouse price
Next, establish a system of equations, keeping in mind that “70% off” is the same as 100% – 70% = 30%, or 0.3, of the original price:
\(0.3J + 12 = 0.6B\)
\(0.3J + 0.6B = 84\)
Now use whatever strategy you’re most comfortable with to solve a system of equations—for example, aligning the equations and then subtracting them:
\(0.3J + 12 = 0.6B\)
\(0.3J - 84= -0.6B\)
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\(0 +96=1.2B\)
\(B=80\)
You can plug the price of the blouse back into the original equation to get the price of the jeans:
\(0.3J + 12 = 0.6B\)
\(0.3J + 12 = 48\)
\(0.3J = 36\)
\(J = 120\)
Alternatively, you could first figure out the price of the discounted jeans, x, with this equation:
\(x + (x + 12) = 84\)
\(2x + 12 = 84\)
\(2x = 72\)
\(x = 36\)
Then plug that discounted price into the equation discounted price = original price × (100% – percent discount):
\(36 = 0.3P\)
\(360 = 3P\)
\(120 = P\)
Hence option D is correct!
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