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