danlew wrote:
The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?
A) 100
B) 103
C) 105
D) 107
E) 110
Here's a solution that uses
two variables:
The ratio of blue to black jeans at a certain shop is 15:16Let B = number of blue jeans PRESENTLY in the shop
Let K = number of black jeans PRESENTLY in the shop
So, we can write: B/K = 15/16
Cross multiply to get:
16B = 15K If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. So, B = number of blue jeans in the shop AFTER 35 black jeans are added
And K + 35 = number of black jeans in the shop AFTER 35 black jeans are added
So, we can write: B/(K + 35) = 15/21
Cross multiply to get: 21B = 15(K + 35)
Expand: 21B = 15K + 525
Subtract 525 from both sides to get:
21B - 525 = 15KHow many blue jeans does the shop have?We now have the following system of equations:
16B = 15K21B - 525 = 15KSince both equations are set equal to 15K, we can write: 16B = 21B - 525
Subtract 21B from both sides: -5B = -525
Divide both sides by -5 to get: B = 105
Answer:
Cheers,
Brent
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