Five Years Ago, Amy Was Three Times As Old As Mike. If Mike Is 10 Years Old Now, How Old Is Amy?

What should come next in the following sequence?
64a, 55b, 46c, 37d, 28e, ?

19f, 10g, 1h

The pattern is descending increments of 9 followed by the first letter, second letter, third letter, and so on.

Which of the following is equivalent to 4*4* 4*4?

$ 4^4 $

An exponent is a method of indicating repeated multiplication. For example, 4*4* 4*4 can also be expressed as $4^4$, which is also known as “4 to the fourth power.” The small number written slightly above and to the right of a number is the exponent, and it indicates the number of times you multiply the number it accompanies by itself.

Terri has a jar of orange, blue, green, and red chocolate candies. In the jar are 75 orange candies, 62 blue candies, and 52 green candies. If there is a total of 252 candies in the jar, what is the probability that Terri will pick a red candy?

1/4

To solve this problem, first find the number of red candies in the jar by adding the numbers of all the other candies together, then subtracting from the total. 75 orange + 62 blue + 52 green = 189 candies.
252 – 189 = 63 red candies.
Probability is the chance that a certain event will happen. Since there are 63 red candies out of a total of 252 candies, divide 63 by 252. Reduce the fraction by dividing the numerator and denominator by 63. 63/252 = 1/4

A man invested $150 in the stock market. During the first week, he lost $45. During the second week, he tripled his money. How much does he have at the end of the second week?

$315

First, calculate how much he had at the end of the first week: $150 – $45 = $105
Since he tripled his money, it is then necessary to multiply this value by 3:
105 × 3 = 315

At the arcade, Nick spent 203 tokens on video games in seven days. Each day he spent five more tokens than the previous day. How many tokens did Nick spend on the third day at the arcade?

24 tokens

Let x = the number of tokens Nick spent on day 1. Set up the following equation and solve for x: x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) + (x + 30) = 203
7x + 105 = 203
x = 14 tokens . We know Nick spent 14 tokens on the first day. To find what he spent on the third day, add 10 tokens to get 24 tokens.

Rachel is driving to visit her mother, who lives 250 miles away. How long will the drive be, round-trip, if Rachel drives at an average speed of 40 mph?

750 minutes

The distance from Rachel’s house to her mother’s house is 250 miles, so round-trip, the distance is 500 miles. Plug this into the distance formula:
d = rt
500 = 40t
500 ÷ 40 = t
12.5 = t
It takes Rachel 12.5 hours to make the round-trip drive. Multiply by 60 to find the answer in minute
12.5 × 60 = 750 minutes.

A child is selling bars for a school fundraiser. He starts with 65. If he has 13 left, how many did he sell?

52

To calculate how many bars the child sold, subtract the number he has left (13) from the number he had originally (65): 65 – 13 = 52

Which of the following statements is true?

If a number is divisible by 2 and 3, it is also divisible by 6.

It is true that if a number is divisible by both 2 and 3, it is also divisible by 6. For example, 108 is divisible by 2 (108 ÷ 2 = 54) and by 3 (1 + 0 + 8 = 9 ÷ 3 = 3), and therefore is also divisible by 6.

How many prime numbers are there between 25 and 35, inclusive?

2

Prime numbers are not divisible by anything other than themselves and 1. The only prime numbers in this set are 29 and 31. 25, 30, and 35 can be excluded because they are divisible by 5. 26, 28, 30, 32, and 34 are divisible by 2. 27, 30, and 33 are divisible by 3.

Convert 0.23 to a fraction

$\frac{\mathrm{23} }{\mathrm{100} } $

When a number is divided by a multiple of 10, simply move the decimal one position to the left for every zero. We can take each answer to find out which one is correct.
$23 \div 100 = 0.23$ (move decimal 2 positions to the left)
$ 23 \div 1.000 = 0.023$ (move decimal 3 positions to the left)
23/10.000 = 0.0023 (move decimal 4 positions to the left)
$23 \div 100.000 = 0.00023$ (move decimal 5 positions to the left)
Therefore, 0.23 converted to a fraction is $\frac{\mathrm{23} }{\mathrm{100} } $

A woman owns a dog walking business. If 2 workers can walk 8 dogs, how many dogs can 3 workers walk?

12

First, figure out how many dogs each worker can walk: 8÷2=4 dogs
Then, multiply this number by 3 to find out how many dogs 3 people can walk: 4×3=12

A tiger in a zoo has consumed 120 pounds of food in 10 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumption be 168 pounds?

4

If the tiger has consumed 120 pounds of food in 10 days that's 120/10 = 12 pounds of food per day. The tiger needs to consume 168 - 120 = 48 more pounds of food to reach 168 pounds total. At 12 pounds of food per day that's 48/12 = 4 more days.

Solve the following: $39 \div (3+10)-3 \times 7$

-18

Solve by using the order of operations. It’s easy to do if you remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
$39 \div (3+10)-3 \times 7 = 39 \div 13-3 \times 7$
$ = 39 \div 13-21 = 3-21 = -18$

Five years ago, Amy was three times as old as Mike. If Mike is 10 years old now, how old is Amy?