Which fraction is a unit rate you can use to solve a ratio problem
A:27/1
B:7/5
C:1/27
D:3/4
Jamal is creating toys to sell. He is averaging 8 toys every 5 days. If he continues at this rate, how many days will it take to fill an order of 75? Round to the nearest whole number of days.
A: 10 days
B: 120 days
C: 375 days
D: 47 days
Ramon makes 33 donuts every 7 hours. Using a unit rate, determine how many whole donuts he would make in 5 hours. (1 point)
Responses
A: 1
B: 23
C: 165
D: 23.57
1.
You can write any rate as a unit rate by reducing the fraction so it has a 1 as the denominator or second term.
27 / 1
A:1
2.
5 / 8 = 75 / x
Cross multiply.
5 x = 600
x = 600 / 5 = 120
B:120
3.
33 / 7 = x / 5
Cross multiply.
165 = 7 x
7 x = 165
x = 165 / 7 = 23.57
D:23.57
To solve a ratio problem, you need to find a fraction that represents the unit rate. The unit rate is a comparison of two different quantities with a denominator of 1.
In the first question, Jamal is creating toys at an average rate of 8 toys every 5 days. To find the unit rate, divide the number of toys (8) by the number of days (5).
The unit rate is 8/5.
Now, let's use the unit rate to solve the problem. We need to find out how many days it will take to fill an order of 75 toys if Jamal continues at the same rate.
To do this, we can set up a ratio:
8/5 (toys per day) = 75 (total toys) / x (number of days)
To solve for x (number of days), we cross multiply:
8x = 5 * 75
8x = 375
Now, divide both sides of the equation by 8 to solve for x:
x = 375 / 8
Calculating this gives us x = 46.875. Since we need to round to the nearest whole number of days, the answer is approximately 47 days. Therefore, the correct answer is 47 days (option D).
In the second question, Ramon makes 33 donuts every 7 hours. To find the unit rate, divide the number of donuts (33) by the number of hours (7).
The unit rate is 33/7.
To determine how many whole donuts Ramon would make in 5 hours, multiply the unit rate (33/7) by the number of hours (5):
(33/7) * 5 = 165/7
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 1 in this case:
165/7 ÷ 1/1 = 165/7
Therefore, Ramon would make 165/7 whole donuts in 5 hours. To find the whole number of donuts, divide the numerator (165) by the denominator (7):
165 ÷ 7 = 23 remainder 4
The answer is 23 with a remainder of 4. Since we're looking for whole donuts, disregard the remainder. Thus, Ramon would make 23 whole donuts in 5 hours. Therefore, the correct answer is 23 (option B).
To solve a ratio problem, you need to find a fraction that represents a unit rate. A unit rate is when the numerator and denominator of the fraction represent the same quantity.
For the first question, the fraction that represents a unit rate is A: 27/1. This fraction means that for every 1 unit of the quantity, there are 27 units of the same quantity.
Now, let's solve the second question step-by-step using the given unit rate.
Jamal is creating 8 toys every 5 days. We can write this as a ratio: 8 toys / 5 days.
To find out how many days it will take to fill an order of 75 toys, we set up a proportion:
8 toys / 5 days = 75 toys / x days
Cross multiply:
8x = 375
Now, we solve for x:
x = 375 / 8
x ≈ 46.9
Since we need to round to the nearest whole number of days, the answer is 47 days. Therefore, the correct answer is D: 47 days.
For the third question, to find out how many whole donuts Ramon would make in 5 hours, we use the given unit rate of 33 donuts every 7 hours.
First, we determine the unit rate:
33 donuts / 7 hours = 4.71 donuts/hour
Now, we multiply the unit rate by the number of hours in question (5 hours):
4.71 donuts/hour * 5 hours ≈ 23.57 donuts
Since we are asked to determine the number of whole donuts, the closest whole number is 24. Therefore, the correct answer is D: 23 (rounded to 24 donuts).