1.
Write the following ratio in simplest form: 32 min:36 min
8:9
8:36
32:9
128:144
2.
Marie saved $51. On Wednesday, she spent $8 of her savings. What ratio represents the portion of her total savings that she still has left?
43:8
8:51
43:51
59:51
3.
The price of 8.4 ounces of crackers is $2.42. What is the unit price? Round your answer to the nearest cent.
$0.15 per ounce
$3.47 per ounce
$28.81 per ounce
$0.29 per ounce
4.
Jonah needs to purchase 30 juice packs for his class. While shopping, Jonah discovers the following prices for comparable juice packs. Which offers the best unit price?
15 packs for $3.95
5 packs for $2.20
20 packs for $6.20
10 packs for $3.20
5.
Solve the proportion. Where necessary, round to the nearest hundredth.
8/2 = x+3/4
13
1
7
16
6.
A dozen apples cost $2.55. At this rate, how much would 8 apples cost?
$20.40
$3.83
$0.21
$1.70
7.
Use cross products to determine which of the following pairs of ratios cannot form a proportion. (1 point)
1/3, 3/9
2/3, 4/9
2/3, 4/6
1/3, 2/6
8.
Solve the following proportion.
2/15 = 13/x
390
1.73
2.31
97.5
10. Triangle A and Triangle B are similar. The perimeter of Triangle A is 15 m and perimeter of Triangle B is 30 m. What is the scale factor of Triangle B to Triangle A?
a. 1 : 2
b. 2 : 1
c. 3 : 2
d. 4 : 3
1.A
2.A
3.B
4.A
5.C
6.D
7.B
8.B
9.A
10.A
It helps to indicate each answer WITH the question e.g., ***.
1. yes
2. No
3. No
4. Yes
5. Typo?
6. Yes
7. Yes
8. No
10. Yes
1. To find the simplest form of the ratio 32 min:36 min, you need to divide both numbers by their greatest common divisor. In this case, the greatest common divisor of 32 and 36 is 4. So, you divide both numbers by 4 and get 8 min:9 min. Therefore, the simplest form is 8:9.
2. Marie saved $51 and spent $8, so the portion of her total savings that she still has left is $51 - $8 = $43. The ratio representing this is 43:51. Therefore, the answer is C.
3. To find the unit price, you divide the total price ($2.42) by the number of ounces (8.4). So, $2.42 ÷ 8.4 ≈ $0.29 per ounce. Therefore, the unit price is $0.29 per ounce.
4. To find the best unit price, you need to compare the prices per juice pack.
- 15 packs for $3.95 gives a unit price of $3.95 ÷ 15 ≈ $0.26 per pack.
- 5 packs for $2.20 gives a unit price of $2.20 ÷ 5 = $0.44 per pack.
- 20 packs for $6.20 gives a unit price of $6.20 ÷ 20 = $0.31 per pack.
- 10 packs for $3.20 gives a unit price of $3.20 ÷ 10 = $0.32 per pack.
Therefore, the best unit price is 15 packs for $3.95, which gives a unit price of $0.26 per pack.
5. To solve the proportion 8/2 = (x+3)/4, you cross-multiply. This means you multiply 8 by 4 and x+3 by 2. So, you have 8 * 4 = 2 * (x+3). Simplifying, you get 32 = 2x + 6. Subtracting 6 from both sides, you have 26 = 2x. Dividing both sides by 2, you get x = 13. Therefore, the answer is 13.
6. If a dozen apples cost $2.55, then one apple costs $2.55 ÷ 12 = $0.21. Therefore, the cost of 8 apples would be $0.21 * 8 = $1.70.
7. To determine which pairs of ratios cannot form a proportion using cross products, you multiply the first number of the first ratio with the second number of the second ratio, and then multiply the second number of the first ratio with the first number of the second ratio. If the cross products are equal, the ratios can form a proportion, otherwise, they can't.
Let's test each pair of ratios:
- 1/3 * 4/6 = 4/18 = 2/9
- 3/9 * 2/6 = 6/54 = 1/9
Both cross products are not equal, so the pair 2/3, 4/6 cannot form a proportion. Therefore, the answer is B.
8. To solve the proportion 2/15 = 13/x, you cross-multiply. This means you multiply 2 by x and 15 by 13. So, you have 2x = 15 * 13. Simplifying, you get 2x = 195. Dividing both sides by 2, you get x = 195/2 ≈ 97.5. Therefore, the answer is 97.5.
10. To find the scale factor of Triangle B to Triangle A, you divide the perimeter of Triangle B by the perimeter of Triangle A. So, 30 m ÷ 15 m = 2. Therefore, the scale factor is 2:1. Therefore, the answer is b.