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SAT Math 1.3 Numbers and Operations. x and y must be which of the following?
SAT Math 5.7 Numbers and Operations 194 Views
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Description:
SAT Math 5.7 Numbers and Operations
Transcript
- 00:03
Here’s your shmoop du jour, brought to you by ACDC.
- 00:06
Not a line segment, but some of their songs had good lines…
- 00:14
Points A, B, C, D, and E lie on a straight line. C is the midpoint of AE,
- 00:20
D is the midpoint of CE, and B is the midpoint of AD.
- 00:25
If AB is equal to 6, what is the length of AE?
Full Transcript
- 00:31
Sometimes…it helps if we sketch out the problem…like we’ve done here.
- 00:35
We’re also going to label each segment with what fraction of the AE line it is.
- 00:40
So AC is 1/2 of AE.
- 00:44
CD is 1/4 of AE.
- 00:51
AC + CD makes AD, so AD is 1/2 of AE + 1/4 of AE.
- 00:59
With the addition worked out, AD is 3/4 of AE.
- 01:02
The problem tells us that AB is 6, and AB + AB is AD because B is the midpoint of AD.
- 01:09
This means that the length of AD is 12.
- 01:13
We also know that AD is 3/4 of AE, which allows us to write a short equation.
- 01:17
3/4 times AE = 12. So multiply both sides by the reciprocal of 3/4…or 4/3.
- 01:25
…to get that the length of AE is 16.
- 01:28
And we're done.
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