Solving Problems Using Proportions
QUESTION 1
Choose the correct option.
"To prepare a banana and strawberry juice, how many grams of bananas have to be mixed with 100 grams of strawberry to get a 20% banana juice?"
To solve this problem, Mohammed and Ameen set up different proportions:
Mohammed set the proportion as:
x/(x + 100) = 20/100
Ameen set the proportion as:
x/100 = 20/80
Who is correct? Justify.
1. Neither is correct; the proportion should be
x/(x+100) = 20/80
2. Only Mohammed is correct as he set the proportion as
part/whole = percentage/100
3. Both are correct. They used two different methods of solving a percent problem using proportion. ✓
4. Only Ameen is correct because he found the percentage for the strawberry and then set the proportion.
QUESTION 2
Choose the correct option.
Saad was given this problem in a test:
"A simple salad is made of yogurt and cucumbers. How many grams of yogurt should be added to 600 grams of cucumbers to make a 40% by weight yogurt salad?"
Saad was nervous as he had a very short time left for this question.
Which of the proposed methods will allow Saad to solve the problem in the shortest time?
1. Saad should set the proportion as
x/60 = 40/600
, and use the cross products property to solve for x
2. Saad should set the proportion as
x/600 = 40/60
, and use the cross products property to solve for x ✓
3. Saad should set the proportion as
x/100 = (x+600)/40
, and use the cross products property to solve for x
4. Saad should set the proportion as
x/(x + 600) = 40/100
, and use the cross products property to solve for x
QUESTION 3
Choose the correct option.
Jamal was given this problem:
"A typist can type 212 words in 4 minutes. Find the number of words he can type in 3 minutes."
Jamal set up this proportion as
212 / 4 = x / 3
and concluded that the typing speed is around 160 words in 3 minutes.
Is Jamal correct? Justify.
1. Jamal is not correct because 212 and 160 are not multiples of 3.
2. Jamal is not correct because if cross products property is applied, the result is
4x = 636
,and if you multiply 4 by 160, you will get a zero in the units digit, not a 6.
3. Jamal is correct because he set the proportion as an equation with two ratios
having matching units:
212 words / 4 minutes = x words / 3 minutes
and rounded the solution of this proportion correctly. ✓
4. Jamal is correct because 212 and 160 are multiples of 4.
QUESTION 4
Choose the correct option.
A 220 ml soft drink is labeled as "11% sugar," which means there are 11 grams of sugar in 100 ml of soft drink.
Salma wanted to check if this label is correct. She correctly added up the weights of the sugar ingredients listed on the label and found them to be 22 grams.
She set up the proportion
11/100 = x/220
and concluded that the label is correct.
Is Salma right? Justify.
1. Salma is right because she set the proportion correctly, and the correct solution to this proportion is
x= 22
2. Salma is not right because when solving the proportion for x, it is not equal to 22. ✓
3. Salma is right because 22 is a multiple of 11 and a divisor of 220.
4. Salma is not right because she set the part of the soft drink in the proportion to be x, while it is given that it is 22 grams.