Ratio Word Problem

HornetMathRIII

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Sep 16, 2012
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I am spacing on how to go about solving this other than just guess and check. Any help is appreciated.

The ratio of whats to hows was 7 to 3, and thrice the number of hows exceeded twice the number of whats by -40. How many were whats?

Solution is whats = 56 and hows = 24 but how do you get the factor of 8 that each is multiplied by?
 
I am spacing on how to go about solving this other than just guess and check. Any help is appreciated.

The ratio of whats to hows was 7 to 3, and thrice the number of hows exceeded twice the number of whats by -40. How many were whats?

Solution is whats = 56 and hows = 24 but how do you get the factor of 8 that each is multiplied by?

Assume

# of whats = W

# of hows = H

Then:

The ratio of whats to hows was 7 to 3W/H = 7/3 → W = 7/3 * H ......................................... (1)


thrice the number of hows exceeded twice the number of whats by -40
→ 3 * H = 2 * W + (- 40) → 3 * H = 2 * 7/3 * H - 40

Finish it......
 
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