In a competition, three teams, A, B and C, scored a total of 150 points. If A scored 40% of this total and B scored four times as many points as C, what was the number of points scored by B?

For 3 shifts, the worker collects 14 devices. He collected a batch of devices in 18 shifts. How many devices were there in this batch?

84

Step 1: Interpret the Problem and Set Up a Proportion
In this problem, we know that 14 devices were collected in 3 shifts. We are trying to find the number of devices that were collected over 18 shifts.
When we set up the proportion, the units must match. Since we are dealing with devices per shift, the number of devices will be in the numerator and shifts will be in the denominator.
What is missing is the number of devices.
So we have:
$\frac{\mathrm{14 devices}}{\mathrm{3 shifts}} = \frac{\mathrm{x devices}}{\mathrm{18 shifts} }$
$\frac{\mathrm{14} }{\mathrm{3} } = \frac{\mathrm{x} }{\mathrm{18} }$
Step 2: Cross Multiply & Solve the Equation
To find the X, we multiply one denominator by the opposite numerator.
14 × 18 = 3 × x
This gets simplified to:
252 = 3x
Now we can solve for x:
$\frac{\mathrm{252} }{\mathrm{3} } = \frac{\mathrm{3x} }{\mathrm{3} }$
$252 ÷ 3 = 84$
x = 84
There were 84 devices in the batch.

Kyra has a budget of 300 dollars for her holiday spending. Kyra decides to buy shoes for her grandchildren. If each pair of shoes costs 40 dollars, and Kyra has n grandchildren, which of the following inequalities represents Kyra’s budget constraint?

$40n \leq 300$

If Kyra buys n pairs of shoes at a cost of 40 dollars each, she pays 40n dollars. Since she only has 300 dollars to spend, 40n dollars must be less than or equal to 300 dollars: $40n \leq 300$

A father is planning a birthday party for his son. He is expecting a total attendance of 7 adults and 13 children. Food costs will be $11.00 for each adult and $5.00 for each child. He will also need to spend $2.00 per child for party favors. Which of the following is the total cost of the birthday party?

$168.00

The cost for each adult is $11.00 and there are 7 adults: 7 × 11=77
The cost for each child is $7.00 ($5.00 for food plus $2.00 for the party favors) and there are 14 children: 13 × 7=91
Total Cost=$77+$91=$168

You have $100 to spend. You pick out two items to purchase. The first item is $64.57. The second item is $26.82. If you buy both of these items, how much money will you have left?

$8.61

The two items total $91.39 ($64.57+$26.82=$91.39). Therefore you have $100-$91.39=$8.61 left.

Solve for x: 5x − 4 = 3(8 + 3x)

-7

Isolate the variable x on one side of the equation.
5x − 4 = 3(8 + 3x)
5x − 4 = 24 + 9x
−4 − 24 = 9x − 5x
−28 = 4x
$\frac{-28}{4} = \frac{4x}{4}$
x = −7

Out of 1560 students at Ward Middle School, 15% want to take French. Which expression represents how many students want to take French?

1560 × 0.15

Use the formula for finding percentages.
Express the percentage as a decimal.
part = whole × percentage = 1560 × 0.15

What is the area of a circle with a radius of 9 in? (Use 3.14 for π)

254.34 in²

Remember the formula for the area of a circle:
πr² = area
Or:
π × r × r = area
Which stands for:
π(pi = 3.14) × radius × radius
Step 1: Substitute Our Numbers Into the Equation
So let’s look at our equation:
π × r × r
The problem has told us to use 3.14 for π and we can see that our radius is 9 inches.
Now our equation looks like this:
3.14 × 9 in × 9 in
Step 2: Solve
Now that we have substituted in our numbers, we can solve it.
Remember, with decimals, we pretend as if the decimals are not there. We do not line up numbers by their decimal point.
1 3
3.14
× 9
2826
Since there are a total of 2 numbers to the right of the two decimal points in the problem, there will be 2 numbers that are behind the decimal in the product. Therefore, the decimal point goes between the number 8 and the second number 2.
28.26 in
Now we multiply the 28.26 and the 9. We do not line up numbers by their decimal point.
72 5
28.26
× 9
25434
Since there are a total of 2 numbers to the right of the two decimal points in the problem, there will be 2 numbers that are behind the decimal in the product. Therefore, the decimal point goes between the first number 4 and 3.
254.34 in²
So, the area is 254.34 in²

Joe makes $20 an hour and Tim makes $30 an hour. How many hours more than Tim must Joe work to earn the same amount Tim makes in 4 hours?

2

Tim will make $120 in 4 hours and Joe will need 6 hours to make $120. So 6 − 4 = 2

If 4 people can stain a deck in 2 days, how many people would be required to stain the deck in only 1 day?

8

If it requires 4 people for 2 days, then it would require 8 people for 1 day.

For the following numbers, which is the CORRECT order of the variables from smallest to largest?
P = 0.0002
Q = -0.02
R = 0.2
S = -200
T = 0.5

SQPRT

To solve these questions, we need to put the numbers in increasing order. This will allow you to easily compare which numbers are larger or smaller.
Then place them in order from least to greatest (like you would see on a number line):
-200
-0.02
0.0002
0.2
0.5
S
Q
P
R
T

Express this number as a percentage: $\frac{\mathrm{15} }{\mathrm{49}}$

30.6%

$\frac{\mathrm{15} }{\mathrm{49}}$ = 0.306
Multiply 0. 306 by 100% to express as percentage
$0.306 \times 100$ = 30.6%

The length of Janelle’s Garden is 200 m. What is the length of Janelle’s garden in feet? (Round to the nearest hundredth of a foot if necessary)

656.17 feet.

Step 1:
Recall that 1 foot = 0.3048 meters. We can use this information to set up the following proportionality equation:
(1 foot)/(0.3048 meters) = (x feet)/(200 meters)
Step 2:
We can then use cross multiplication to solve for the missing term:
(0.3048 meters) × (x feet) = (1 foot) × (200 meters)
0.3048x = 200 feet
Step 3:
Finally, we can divide both sides of the equation by 0.3048 to solve for x:
(0.3048x)/0.3048 = 200 feet/0.3048
x = 656.17 feet

Solve the equation and choose the BEST answer: $\frac{\mathrm{9} }{\mathrm{b}} = \frac{\mathrm{b} }{\mathrm{4}}$

6

Cross-multiply: $9 \times 4 = b \times b$
$36=b^2$
Then, find the square root of both sides:
The actual square root of $b^2$ is $\pm b$ and the actual square root of 36 is $\pm b$, so:
$b= \pm 6$
Of the answer choices for this question, 6 is the best choice since it is the only one that is true about the equation.

Simplify the expression below. $(5x−1)(3x+2)$
Which of the following is CORRECT?

$15x^2+7x-2$

The “FOIL method” is the easiest way to remember how to multiply two-termed expressions. Multiply the First two terms, then the Outer two terms, then the Inner two terms, and then the last two terms, then sum all four to arrive at the answer:
$15x^2+10x-3x-2=15x^2+7x-2$

A woman has 8 black shoes, 5 brown shoes, 2 red shoes, and 5 boots. What percentage of her collection are boots?

25%

Since she has 20 overall items in her collection, boots make up 25% of her collection ($ \frac{\mathrm{5} }{\mathrm{20}} = 25 \% $)

In a competition, three teams, A, B and C, scored a total of 150 points. If A scored 40% of this total and B scored four times as many points as C, what was the number of points scored by B?

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In a competition, three teams, A, B and C, scored a total of 150 points.
If A scored 40% of this total and B scored four times as many points as C, what was the number of points scored by B?