There are 2 questions with a total of 5 parts. Make sure you label and answer all parts. Explain your answers. Answers without explanation will receive no credit.
1. Yolanda has finished 45% of the homework problems she was assigned. So far she has finished 27 problems.
A. Write 45% as a rate per 100 (fraction) and then reduce the fraction to lowest terms.
B. How many problems was Yolanda assigned? Justify your answer.
C. How many problems does Yolanda still have to do? Show your work.
2. The farmer's market is selling apples today at a price of 6 for $8.40.
A. What is the unit rate for each apple? Show your work.
B. Emma needs to buy 26 apples for the apple butter. How much will 26 apples cost at the farmer's market? Explain your reasoning.
A. 45% can be written as a rate per 100 (fraction) as 45/100. This fraction can be reduced to 9/20.
B. Yolanda was assigned 60 problems. This can be determined by taking the total number of problems she has finished (27) and adding it to the number of problems she still needs to do (33).
C. Yolanda still has to do 33 problems. This can be determined by taking the total number of problems she was assigned (60) and subtracting it from the number of problems she has finished (27).
A. The unit rate for each apple is $1.40. This can be determined by taking the total cost of the apples ($8.40) and dividing it by the number of apples (6).
B. 26 apples will cost $36.40 at the farmer's market. This can be determined by taking the unit rate for each apple ($1.40) and multiplying it by the number of apples (26).
so whats the answer??????
1.
A. To write 45% as a rate per 100, we divide 45 by 100:
45/100 = 9/20.
To reduce this fraction to lowest terms, we divide the numerator and denominator by their greatest common divisor, which is 9:
9/20 ÷ 9/9 = 1/2.
Therefore, 45% as a rate per 100, reduced to lowest terms, is 1/2.
B. To find the number of problems Yolanda was assigned, we use the proportion:
27 (problems completed) is to 45% (total problems) as x (total problems) is to 100 (total).
This can be written as:
27/45% = x/100.
To solve for x, we cross-multiply:
27 * 100 = 45% * x.
Dividing both sides by 45%, we get:
27 * 100 ÷ 45% = x.
Calculating this, we find:
27 * 100 ÷ 45% = 60.
Therefore, Yolanda was assigned 60 problems.
C. To find out how many problems Yolanda still has to do, we subtract the number of problems she has finished from the total number of problems assigned.
Total problems assigned - Problems finished = Problems left to do.
Therefore, 60 (total problems assigned) - 27 (problems finished) = 33 problems left to do.
2.
A. To find the unit rate for each apple, we divide the total cost by the quantity:
$8.40 / 6 apples.
Dividing $8.40 by 6, we find:
$8.40 ÷ 6 = $1.40.
Therefore, the unit rate for each apple is $1.40.
B. To find the cost of 26 apples at the farmer's market, we multiply the unit rate by the quantity:
$1.40 * 26 apples.
Multiplying $1.40 by 26, we find:
$1.40 * 26 = $36.40.
Therefore, 26 apples will cost $36.40 at the farmer's market.
1. Yolanda has finished 45% of the homework problems she was assigned. So far she has finished 27 problems.
A. To write 45% as a rate per 100, we divide 45 by 100: 45/100 = 0.45. This means that Yolanda has completed 0.45 of the total problems assigned to her. To reduce this fraction to lowest terms, we notice that both numerator and denominator are divisible by 5. Therefore, the fraction can be reduced to 9/20.
B. To find out how many problems Yolanda was assigned, we can set up a proportion. Since she has completed 0.45 (or 9/20) of the assigned problems, we can write the following proportion:
0.45/1 = 27/x
Solving this proportion for x, we can cross multiply: 0.45 * x = 1 * 27. Simplifying, we get 0.45x = 27. Dividing both sides by 0.45, we find x = 27 / 0.45 = 60. Yolanda was assigned 60 problems.
C. To find out how many problems Yolanda still has to do, we can subtract the number of problems she has already finished from the total number of problems assigned. This can be written as:
Total problems - Problems finished = Problems remaining
60 - 27 = 33
Therefore, Yolanda still has 33 problems to do.
2. The farmer's market is selling apples today at a price of 6 for $8.40.
A. To find the unit rate for each apple, we divide the total cost by the number of apples: $8.40 / 6 = $1.40. Therefore, the unit rate for each apple is $1.40.
B. To find out how much 26 apples will cost at the farmer's market, we can use the unit rate we calculated earlier. Since each apple is priced at $1.40, we can multiply this price by the number of apples needed:
$1.40 * 26 = $36.40
Therefore, 26 apples will cost $36.40 at the farmer's market.