Jack is twice as old as Lacy. In three years, the sum of their ages will equal to 54. Write the equation and show all steps to solve.

Mathematics · Middle School · Tue Nov 03 2020

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Given the statement:
Jack is twice as old as Lacy. In three years, the sum of their ages will equal to 54.

Representation:

Let x = Lacy's Age

2x = Jack's Age

Solution:

Since the sum of Lacy's Age and Jack's Age in 3 years is equal to 54, then we can represent it in an equation as.

( x + 3 ) + (2x + 3) = 54

Now we need to solve for x in order to determine their ages.

x + 3 + 2x + 3 = 54

 3x + 6 = 54

Transpose 6 on the other side of the equation, note that when transposing a number, the sign changes.

3x = 54 - 6

3x = 48

Divide both sides by 3 in order to get the value of x.

x = 16

2x = 32

Lacy's Age = 16

Jack's Age = 32

Check: 

(16 +3) + (32 + 3) = 54

19 + 35 = 54

54 = 54

Final answer:

Lacy's Age = 16

Jack's Age = 32