Daren is 3 years older than Tom. 3 years ago Leah will be 14 less than 3 times Darren's age. 5 years ago, Leah was 2 years less than 2 times Tom. How old will Leah be 4 years from now?

answer

5

set up equations

daren is 3 years older than tom

D = 3 + T

3 years ago leah will be 14 less than 3 times darren's age

L - 3 = 3(D - 3) - 14

L - 3 = 3D - 9 - 14

L = 3D - 9 - 14 + 3

L = 3D - 20

5 years ago, leah was 2 years less than 2 times tom

L - 5 = 2(T - 5) - 2

L - 5 = 2T - 10 -2

L = 2T - 10 - 2 + 5

L = 2T - 7

find leah's current age

set L = 3D - 20 and L = 2T - 7 equal to each other

3D - 20 = 2T - 7

plug 3 + T into D using the equation D = 3 + T

3D - 20 = 2T - 7

3(3 + T) - 20 = 2T - 7

9 + 3T - 20 = 2T - 7

T = - 7 - 9 + 20

T = 4

plug T back into L = 2T - 7 to find leah's current age

L = 2T - 7

L = 2 * 4 - 7

L = 8 - 7

L = 1

leah's age 4 years from now

add 4 to leah's current age

1 + 4 = 5

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