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SAT Math 1.3 Algebra and Functions. How many 16 oz. bottles did she buy?
FYI: cats don't like to get wet. Okay, so that fact won't be relevant every time you solve trig equations, but it happens to be this time.
SAT Math 4.4 Algebra and Functions 197 Views
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Description:
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.
Full Transcript
- 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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