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3 years ago

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

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

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.

Check

In 8 years, he will be 22 and she will be 44, twice his age.

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 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.

Check

10 years from now, April will be 28. That is 4 years more than 2·12 = 24.

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.

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.

We have essentially written our own problem statement here. Your problem statement, and your answer, may vary.

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