Explanation:
The ratio of coloring to white is 1:4.
A total of 12 gallons of colored paint are needed.
Let c represent the amount of coloring in the 12 gallons.
The amount of white is then 12 – c.
Set up the proportion c/12−c= 1?4.
Use cross-multiplication to solve the equation for c.
12–c=4c
12=5c
5c=12
c=12/5=2 2/5
Because of the 1:4 ratio, 3 gallons may seem like a correct answer (divide 12 by 4). It is not correct because the total
amount of paint is 12 gallons. If the problem stated that 12 gallons of white paint were used, then 3 gallons would
have been correct. But, if you use 3 gallons of colored paint plus the 12 gallons of white paint, you would use 15 gallons
of paint and that is not what the problem specifies. These problems can be tricky. Be sure to read them carefully.
Explanation:
Ratios can also be written as fractions with the first item in the ratio as the numerator and the second item as the denominator,
as student D has done.
Student A has given a fraction equivalent to the original ratio and is also correct.
The answer given by student B is not an equivalent fraction to the original ratio.
The order of the ratio must be preserved, so student C is incorrect.
Explanation:
54 and 36 are common multiples of 6 and 9, but they are not the least common multiple.
To find the least common multiple, examine the prime factors of 6 and 9:
6 = 2 x 3 and 9 = 3 x 3
6 and 9 share one instance of the prime factor 3, so the least common multiple will contain one 3 coming from the
overlap and the other 3 coming from the prime factorization of 9.
Multiply the prime factors together to compute the LCM:
2 x 3 x 3 = 18
Explanation:
This is a weighted average question. Multiply each score by the percentage of the total that it accounts for:
weighted math score: 89⋅0.35=31.15
weighted science score: 85⋅0.35=29.75
weighted language arts score: 76⋅0.3=22.8
The overall score is the sum of the weighted scores:
31.15+29.75+22.8=83.7, rounded to the nearest whole number, is 84.
Explanation:
129=3×43, so it is not prime.
Explanation:
The discounted price of the boots is b – 0.1b=0.9b.
Similarly, the discounted price of a pair of gloves is g–0.15g=0.85g.
The total cost of 1 pair of boots and 2 pairs of gloves during the sale is
0.9b+2(0.85g)=0.9b+1.7g.
Explanation:
To find the total number of days traveled given the total mileage and the miles per day traveled, divide the total mileage
by the number of days.
This can be seen by looking at the measurable units.
miles÷miles/day = miles⋅days./mile = days
The given unit of the answer is days, so that is what we require. This shows that division was the correct operation to do.
The result is 5.25 days.
He will arrive during the 6th day, because, after 5 days, he still has 0.25 (1/4) of a day of travel remaining. He will arrive after
1/4 of the 6th day has elapsed.
Explanation:
Start with 12x=3x−5
x/2 = 3x−5 Multiply both sides by 2.
x=6x−10 Subtract 6x from both sides.
−5x=−10 Divide both sides by −5
x=2
Explanation:
The distributive property does not work over multiplication or division, so that rules out choices a and d. The distributive
property does work over addition, but choice c should be 6rt(m+2n)=6mrt+12nrt, not 12mnrt. That leaves choice b which
is done correctly.
Explanation:
An average is calculated by dividing a total by the number of items.
In this case, the total sales divided by the number of hours, to give an average of sales per hour. In this case, we know the
number of hours will be 5.
She wants an average of $15 per hour, so that means that totalsales/5 = 15, or totalsales=5⋅15, or $75.
She has $57 in sales after 4 hours, so she must get $18 more in sales to reach $75 by the end of 5 hours.
Explanation:
The probability of a random event is the number of successful possibilities divided by the total number of possibilities.
After Jack has taken the first sock, there are 15 remaining as the total number of possible socks.
Of these, there are 3 remaining blue socks, which represent successful events.
The probability is then:
3/15
which simplifies to:
1/5
Explanation:
The 24 feet of fencing is the perimeter of his garden. For a rectangle with width w and length l, the perimeter P is P=2w+2l.
In this case 2w+2l=24, or w+l=12. He must use a length and width of the rectangle that adds up to 12 feet.
The possible combinations are 1 x 11, 2 x 10, 3 x 9, 4 x 8, 5 x 7, and 6 x 6.
The combination with the highest product, which is the area, is 6 x 6.
A square is a special form of rectangle. The area is 6 x 6 = 36 square feet.
Explanation:
Start by calculating the total number of plants.
31,000×50=1,550,000
Set up a proportion to calculate the number of infested plants.
9/75 = x/1,550,000
x=186,000
Explanation:
The median is the value in the middle. The mean is the average; the sum of all values divided by the number of values.
The results for each set are:
a) {20,23,24,24,29,34,35} The median is 24 and the mean is 27(.)
b) {12,17,22,28,28,33,34} The median is 28 and the mean is 24.9(.)
c) {24,26,29,29,29,34,35} The median is 29 and the mean is 29.4(.)
d) {19,21,27,27,30,34,35} The median is 27 and the mean is 27.6(.)
Explanation:
The two triangles are congruent, so corresponding sides of △ABC are congruent to those of △DEF.
This means both triangles will have the same perimeter: 15+12+9=36
Explanation: A perfect square is a number formed when a whole number is multiplied by itself. The number 169 is formed by 13 multiplied by 13.
Explanation:
Test 1: 37÷55≈67%
Test 2: 47÷72≈65%
Test 3: 41÷64≈64%
Explanation:
An improper fraction has a numerator that is larger than the denominator.
Explanation:
Ratios can also be expressed as fractions, with the first term as the numerator and the second term as the denominator.
The 4 should become the numerator and the 12 should become the denominator.
The result is 4/12.
You can simplify the fraction by dividing the 4 and the 12 by 4.
4÷4=1
12÷4=3
The fraction becomes 1/3
Explanation:
To find a percentage of a number you convert the percent to a decimal and then multiply that by the given number.
To convert the percent to a decimal, you multiply 32×0.01=0.32. Then, you need to take that answer and multiply it
by your original amount of 150.
0.32×150=48
Explanation:
To find the unit rate, you set up a proportion and simplify to find how long it takes to get 1 chapter. You can look at it like this:
3/45 = 1/x
You cross multiply to get
3x=45
Divide both sides by 3 to isolate x.
3x÷3=45÷3
x=15
Explanation:
A factor of a number can evenly divide that number.
Explanation:
In the metric system, weight (technically, mass) is measured in kilograms. Meters and centimeters measure
length. Volume is measured in milliliters.
Explanation:
You start at 32 because 32 is the freezing point of water in Fahrenheit.
First, you subtract 17 from 32:
32−17=15
Next, you add 12 to that result:
15+12=27
Explanation:
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the
numerator. Place this number over the given denominator.
10 3/5
10×5 = 50
50 + 3 = 53
53/5
