Answer:
4. Nelson: 14; Alison: 36
5. May: 12; April: 18
7. Student: 7; Instructor: 27 -- caveat emptor
Step-by-step explanation:
4. Quick answer: The time between Alison being 2 times her son's age (age ratio = 4:2) and 3 times her son's age is 11 years. That means each "ratio unit" stands for 11 years. 3 years ago, when Alison was 3 times her son's age, he was 11 and she was 33. Now, he is 14 and she is 36.
<em>Check</em>
In 8 years, he will be 22 and she will be 44, twice his age.
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If you want to write a system of equations, you can use A for Alison's age and N for Nelson's age.
A+8 = 2(N+8) . . . . relation of ages in 8 years
A -3 = 3(N -3) . . . . relation of ages 3 years ago
We can equate expressions for A:
2(N +8) -8 = A = 3(N -3) +3
2N +8 = 3N -6
14 = N
A = 2(14 +8) -8 = 36
Alison is 36; Nelson is 14.
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5. Quick answer: The sum of ages 6 years from now will be 36. Then April will be twice May's present age. That is, May's present age is 1/3 0f 36 = 12. April is 30 -12 = 18. Now, April is 18 and May is 12.
<em>Check</em>
10 years from now, April will be 28. That is 4 years more than 2·12 = 24.
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Once again, you can write a system of equations:
A + M = 30
A +10 = 2M +4
Again, equating expressions for A, we have ...
30 -M = A = (2M +4) -10
36 = 3M . . . . . simplify, add M+6
12 = M
A = 30 -12 = 18
April is 18; May is 12.
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7. Makes no sense. The first sentence says the age difference is 20 years. The second sentence says the age difference is 5 years. It can't be both. Something is missing somewhere.
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If we assume the word "twice" is missing, then the system of equations for Instructor and Student can be ...
I = S + 20
I + 8 = 2(S +8) +5
Substituting for I, we have ...
S +20 +8 = 2S +16 +5
7 = S . . . . . . subtract S+21
I = 7+20 = 27
The instructor is 27, the student is 7.
<em>Check</em>
In 8 years, the instructor will be 35 and the student will be 15. At 35, the instructor will be 5 years more than twice the student's age.
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We have essentially written our own problem statement here. Your problem statement, and your answer, may vary.
