Question 926444

40. Michael’s age is seven-tenths of Richard’s age. In four years Michael’s age will be eight-elevenths of Richard’s age. How old is Michael now?
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Let Richard's current age, be R
Then Michael's current age = {{{(7/10)R}}}, or {{{7R/10}}}
Therefore, we get: {{{M + 4 = (8/11)(R + 4)}}}
{{{M + 4 = 8(R + 4)/11}}}
{{{11(7R/10) + 44 = 8R + 32}}}
{{{77R/10 - 8R = - 44 + 32}}}
77R - 80R = - 440 + 320 ------ Multiplying by LCD, 10
- 3R = - 120
R, or Richard's current age = {{{(- 120)/(- 3)}}}, or 40 years-old
Michael's current age: {{{(7/10)40}}}, or {{{(7/cross(10))4cross(40)}}}, or {{{highlight_green(28)}}} years-old