Question

Myles and Darrell are brothers and myles is older. When you square Darrell's age and multiply by 2 and subtract from the square of Myles age the result is 6times the difference between their ages. When add Myles and Darrell's age you get 5times the difference between their ages. How old is Darrell and how old is Myles.

Answer 1

Myles is 6 years old and Darrell is 4 years old. We derived this by setting up and solving two algebraic equations based on the relationships given between their ages.

Step-by-step explanation:

We can solve this problem by setting up two equations based on the information given about Myles and Darrell. Let M represent Myles's age and D represent Darrell's age. We have been given two pieces of information to create our equations:

1. When you square Darrell's age and multiply it by 2 and then subtract this from the square of Myles age, the result is 6 times the difference between their ages: M^2 - 2*D^2 = 6*(M - D).
2. When you add Myles and Darrell's age you get 5 times the difference between their ages: M + D = 5*(M - D).

Now, we can solve the equations:

1. First, let's simplify the second equation to express one variable in terms of the other:
2. M + D = 5M - 5D
3. 6D = 4M
4. D = (2/3)M (Equation 2.1)
5. Now, let's substitute D from equation 2.1 into the first equation:
6. M^2 - 2*((2/3)M)^2 = 6(M - (2/3)M)
7. M^2 - (8/9)M^2 = 4M
8. Simplify to find M:
9. (1/9)M^2 = 4M
10. M^2 = 36M
11. M = 6 (since M cannot be 0 because Myles is older than Darrell)
12. Using Equation 2.1, we can now find D:
13. D = (2/3)*6
14. D = 4

Therefore, Darrell is 4 years old and Myles is 6 years old.

Answer 2

Darrell is 12 years old while Darrell is 18 years old

Step-by-step explanation:

Let Myles age be m and Darrell age be d

Single Myles is older, m > d

Square Darrell’s age and multiply by 2; d^2 * 2 = 2d^2

Subtract from the square of Myles age

m^2 - 2d^2

Result is 6 times the difference between their ages;

m^2 - 2d^2 = 6(m-d) •••••••••••(i)

When add Myles and Darrell age

m+ d

you get 5 times the difference between their ages 5(m-d)

m + d = 5(m-d)

m + d = 5m - 5d

5m - m = 5d + d

4m = 6d

m = 6d/4

m = 1.5d or 3/2d ••••••••(ii)

Put ii into i

(3/2d)^2 - 2d^2 = 6(3/2d - d)

9/4d^2 - 2d^2 = 6(1/2)d

Multiply through by 4

9d^2 - 8d^2 = 12d

d^2 = 12d

d^2 - 12d = 0

d(d -12) = 0

d = 0 or d-12 = 0

d = 0 or 12

d = 12 years

The age cannot be zero (if Darrel age is zero, then Myles age will be zero too, this cannot work as their ages are not equal)

So we choose 12 years

Recall ; m = 3/2 d = 3/2 * 12 = 18 years