asked Oct 30, 2015 in Algebra 1 Answers by rootbeer003 (120 points)

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Let the 2 numbers be A and B. A/B=3/5; A+B=136. So B=136-A and we can substitute B in the other equation: A/(136-A)=3/5. Cross-multiply: 5A=3(136-A)=408-3A. 8A=408, A=408/8=51. B=136-51=85. Check the answer: A/B=51/85=3/5. 

In words: This is a problem with two unknowns, A and B, and two equations. We use one equation to write one unknown in terms of the other (B is 136 less A), then we substitute for that unknown in the other equation to give A divided by (136 minus A). That gives us one equation and one unknown, A, where the quotient is equal to three fifths. By cross-multiplying to get rid of the fraction, we arrive at five times A is equal to 3 times B which is known to be 136 less A. Now we collect the A terms together to give 8 times A equal to the product of 3 and 136, that is 408. From this we simply divide 408 by 8 to get A equal to 51, then, by subtracting this value from 136 we get B equal to 85. 51 is 3 times 17 and 85 is 5 times 17 so the quotient is three fifths.

answered Oct 30, 2015 by Rod Top Rated User (442,500 points)

1. Set up the following word problem as an equation and solve. Then write your answer as a complete sentence. The ratio of two numbers is 3 to 5. Their sum is 136. Find the two numbers.

Let there be two numberss a and b. Then

a : b = 3 : 5     their ratio is 3 to 5

a + b = 136     their sum is 136

From the 1st equation, a/b = 3/5, therefore a = (3/5)*b

Substituting for a = (3/5)*b into the 2nd equation,

(3/5)*b + b = 136       mutliply both sides by 5

3b + 5b = 680

8b = 680

b = 85

a = (3/5*b = (3/5)*85 = 3*17

a = 51

The two numbers are: 51 and 85

answered Oct 30, 2015 by Fermat Level 10 User (69,760 points)

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