Can you help me with 4 and 5 and 7 please please

4. Alison is the mother and coach of one of the students, Nelson. In 8 years. Alison will be twice as old u her son will be then. 3 years ago, Alion was 3 times as old as Ndion was then. What are their ages non?

5. April and May are scammates. The sum of their ages now is 30. 10 years from nom, April che older lammate, will be 4 years more than twice May's are now, What are their ages now?

7. A tackwoado instructor is 20 years older than his youngest student. In eight years, the instructor's age will be 5 years more than the student's age then. What are their ages now?

  4. Nelson: 14; Alison: 36

  5. May: 12; April: 18

  7. Student: 7; Instructor: 27   --   caveat emptor

Step-by-step explanation:

4. Quick 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.

Check

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.

5. Quick 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.

Check

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.

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.

Check

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.

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