ShmoopTube

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This question might blow the shmoopiest right off your head.

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A family has three children.

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The sum of the ages of the two youngest children is equal to the age of the oldest child.

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In six years, the youngest child will be half the age of the oldest child,

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and the middle child will be 18.

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What is the current age of the oldest child?

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And here are the potential answers…

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Okay, so we’re given a bunch of info about these three young ruffians,

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and we need to use it to find the current age of the oldest kid.

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Let’s start by assigning some variables.

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We can assign x to the age of the youngest child, and y to the age of the middle child.

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So, we know that x plus y is the age of the oldest child.

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We know that in six years, the youngest child will be half the age of the oldest child.

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Let’s try to write this in mathematical terms.

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The age of the youngest child will be x plus six.

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The age of the oldest child will be x plus y plus six.

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Since the youngest child will be half the oldest child’s age, we can write:

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two times the quantity x plus six equals x plus y plus six.

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This simplifies into two x plus twelve equals x plus y plus six.

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Finally, we can rewrite this as x equals y minus six.

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We know that in six years the middle child will be eighteen years old.

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We can write this as y plus six equals eighteen.

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If we subtract six from both sides, we see that y equals twelve.

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Now we can plug this value for y into our equation for x, x equals y minus six, to find

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that x equals twelve minus six, or six.

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The oldest child’s age is x plus y, so we can

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plug in our values of x and y to find that the oldest child’s age is eighteen.

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The answer is (D).

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