PROBLEMS EXPLAINED

EACH WEEK MORE PROBLEMS WILL BE ADDED AND EXPLAINED

11-14

ACT Challenge Problem 10

15 miles in 2.5 hours

15/2.5 = 6 miles / hour or 6 miles / 60 minutes

now how many minutes to go 1 mile:

1 mile * 60 minutes/6 miles = 10 minutes

or take the 6 miles / 60 minutes and divide both by 6

1 mile / 10 minutes

11-15

ACT Challenge Problem 11

8 Red, 9 yellow, 7 green = 24 total

Want red to be 3/5 probability by adding how many more?

We are starting at 8/24 which simplifies to 1/3 not there yet

so lets take 3/5 so and multiply it to get to possible answers:

6/10 (too small on total marbles)

9/15 (too small)

12/20 (too small)

15/25 (we can't reach that with adding to what we already have)

18/30 (if I add 10 red my total would be 34 so this doesn't work)

21/35 (if I added (21-8) = 13 red then total (24 + 13) = 37)

24/40 (if added (24-8) = 16 red then total (24 + 16) = 40

last one is correct so I need to add 16 reds to get the 3/5 ratio

11-16

ACT Challenge Problem 12

The 2 numbers are (x, y)

CD have 2 points and the mid point is half way between

C = (6, 8)

Mid = (2, 1)

D =

for the x

6 + ? = 2 so the ? = -4 so the mid point subtracted 4 so subtract another 4 to get the D 2-4 = -2

for the y

8 + ? = 1 so the ? = -7 so the mid point subtracted 7 so subtract another 7 to get the D 1-7 = -6

put them together (-2, -6)

11-17

ACT Challenge Problem 13

Setup an equation

for the first 40 hours

$15 * x (x is the hours worked up to 40)

1.5 * $15 * y (y is the hours worked after 40)

pay = $15 * x + 1.5 * $15 * y - deductions

pay = $15 * 40 + 1.5 * $15 * 6 -$117

pay = 600 + 135 - 117 = $618

11-18

ACT Challenge Problem 14

3 bags on Monday for 3 each = 9

4 bags on Wednesday for 2.80 = 11.20

Total = 20.20

7 bags at 2.60 = 18.20

20.20 - 18.20 = $2.00 saved

11-7

ACT Challenge Problem 6

180 * 1/4 (or 180 / 4) = 45 who got A(use a calculator)

180 * 1/3 (or 180 / 3) = 60 who got B

180 - 45 - 60 = 75 who got C

11-9

ACT Challenge Problem 7

f(x) = 3(2^x) so 2 is raised to the x power

x = 0 for 2000, x = 1 for 2001 so for 2006, x = 6

f(6) = 3 * (2^6)

PEMDAS

Do the parenthesis first

Exponent is in the parenthesis so 2^6 = 64

(use calculator. Look for ^ or x^y button)

3* 64 = 192

11-10

ACT Challenge Problem 8

distance / time = speed

distance: at 8 am distance left was 510

at 1 pm distance left was 105

Total distance = 510 - 105 = 405 km

Time: 8am to 1 pm. 5 hours (look at the clock in the room or count the hours in your head)

40 5km /5 hr = 81 km/hr

11-11

ACT Challenge Problem 9

Notice the 2 sides of the smallest triangle. 8 and 16. The right side is 2 x the left. As the angle is the same this ratio will follow all the way down.

7 x 2 = 14

6 x 2 = 12

Then add the left side 16 + 14 + 12 = 42

ACT Challenge Problem 1

This is a easy probability problem. The total number of possible outcomes are 15. It wants to know how likely you are to get a number less than 9. So there are 8 possible numbers that would work. So 8/15 is the answer. If you could you would simplify but not necessary in this problem

ACT Challenge Problem 2

-4x3-12x3+9x2

The problem wants you to simplify. This is testing your knowledge on combining like terms. Combine the -4x3-12x3 because they have the same exponent. So -4 - 12 = -16x3+9x2

Can't do anything with the x2

ACT Challenge Problem 3

x = 2 then 10 + 3 (12/(3x)) = ?

Just plug 2 into x. Remember the if the number is next to a parenthesis just multiply.

10 + 3 * (12/(3 * 2)) = ?

Then follow PEMDAS for order of operation to do first:

Parenthesis, Exponents, Multiply, Divide, Add, Subtract

Parenthesis (do the inner most one first) 3* 2 = 6

10 + 3 * (12/6)) = ?

Parenthesis (do the next one) 12/6 = 2

10 + 3 * 2 = ?

Multiply before Add so: 3 * 2 = 6

10 + 6 = ?

Add 10 + 6 = 16

ACT Challenge Problem 4

| 6 - 4 | - | 3 - 8 | = ?

Absolute value make it positive and kind of acts like parenthesis so do them first

|( 6 - 4 )| = | -2 |

Same for the other absolute value

| 3 - 8 | = | -5 |

So: | -2 | - | -5 |

The bars just make it positive |-2| = 2 and |-5| = 5

So: 2 - 5 = -3

ACT Challenge Problem 5

(4c - 3d) (3c + d) Remember we are multiplying these.

FOIL - First, Outer, Inner, Last

FIRST: 4c * 3c = 12 c2 (you multiply the numbers and combine the variables - for the same combine the 2 c variables to a c2)

SO FAR: 12 c2

Outer: 4c * d = 4cd (can't combine c and d so just keep both)

SO FAR: 12 c2 + 4cd

Inner: (-3d) * 3c = -9cd (keep the negative with the number after it)

SO FAR: 12 c2 + 4cd - 9 cd

Last: (-3d) * d = -3d2

SO FAR: 12 c2 + 4cd - 9 cd - 3d2

Combine like terms (cd):+ 4cd - 9 cd = -5 cd

Answer: 12 c2 - 5 cd - 3d2