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Linear Inequalities Videos 13 videos

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SAT Math 4.4 Algebra and Functions 197 Views


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SAT Math 4.4 Algebra and Functions


Transcript

00:02

This question might blow the shmoopiest right off your head.

00:06

A family has three children.

00:08

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

00:14

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

00:19

and the middle child will be 18.

00:21

What is the current age of the oldest child?

00:23

And here are the potential answers…

00:27

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

00:31

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

00:34

Let’s start by assigning some variables.

00:37

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

00:41

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

00:45

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

00:50

Let’s try to write this in mathematical terms.

00:53

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

00:56

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

00:59

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

01:04

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

01:11

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

01:22

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

01:27

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

01:31

We can write this as y plus six equals eighteen.

01:35

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

01:40

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

01:46

that x equals twelve minus six, or six.

01:50

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

01:53

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

01:59

The answer is (D).

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