Ten years ago, the age of Mark was half of Mary’s age....

Ten years ago, the age of Mark was half of Mary’s age. If the ratio of their present age is 3:4, what will be the total of their present age?

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x = Mary’s age 10 years ago
0.5x = Mark’s age 10 years ago {10 years ago, Mark’s age was half Mary’s}

x + 10 = Mary’s age now {added 10 onto age 10 years ago}
0.5x + 10 = Mark’s age now {added 10 onto age 10 years ago}

Present ages are in a ratio of 3:4. Set up a proportion with the two ages equal to 3/4.

3/4 = (0.5x + 10)/(x + 10)
4(0.5x + 10) = 3(x + 10) {cross-multiplied}
2x + 40 = 3x + 30 {used distributive property}
x = 10 {subtracted 2x and 30 from each side}

x + 10 = 20 {substituted 10, in for x, into x + 10}
0.5x + 10 = 0.5(10) + 10 = 5 + 10 = 15 {substituted 10, in for x, into 0.5x + 10}

Mary is 20 now
Mark is 15 now

Total of ages = 35

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