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?
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) {crossmultiplied} 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 Ask the House
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