# ACT Math: Five Solutions (4/17/15)

Hopefully you were able to find some time and a quiet place this weekend to try our Five Problems for Your Weekend (4/17/15). Below you’ll find the fully worked-out solutions to those problems.

11.  E
In order for Joanna to average 150 for the three games, the total of her three scores must be 3 x 150 = 450. Remember, average problems are very often about the total of the numbers. So far, she has two scores that total 148 + 142 = 290. In the third game, she’ll need to get a score of 450 – 290 = 160.

26.  J
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side (the “TOA” in SOH-CAH-TOA). For angle B that ratio is 12/5.

37.  D
The altitude splits the equilateral triangle into two 30-60-90 special right triangles. You can use what you know about the 30-60-90 triangle to label the other sides of the triangle.

Now use the area formula for a triangle to get your answer.

A = 1/2bh
A = 1/2(8√3)(12)
A = 48√3

42.  G
This problem is all about organizing what you know and what you need to know.

Total Population: 36,000 + 24,000 = 60,000
Votes Needed for Approval: 60,000 x 60% = 36,000
Votes “For” in Allenville: 36,000 x 80% = 28,800
Votes “For” Needed in Barrington: 36,000 – 28,800 = 7,200
Percentage Needed in Barrington:  7,200/24,000 = .3 = 30%

57.  E
In order to get this problem correct, you need to be very good with log rules (if you need quick review of those rules, go here). So let’s see what this problem would look like.

$log_{2}40-log_{2}5=log_{4}x$
$log_{2}\frac{40}{5}=log_{4}x$
$log_{2}8=log_{4}x$
$3=log_{4}x$

Not use what you know about logs to re-write the last equation above as an exponential equation

4³ = x
64 = x

If you have questions about these problems or anything to do with the ACT, send us an email at info@cardinalec.com.