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13 Jul 2021, 08:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
90% (02:01) correct
10%
(02:04)
wrong
based on 96
sessions
History
Date
Time
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Not Attempted Yet
Coffee formerly accounted for 5% of a family’s food budget, while fresh fruits and vegetables accounted for 20%, and meat and dairy accounted for 30%. The family spent the rest of the food budget on fast food and desserts. If the price of coffee doubled and the family reduced the fruit and vegetable share to meet that expense and spend the same overall, the ratio of their new fresh fruit and vegetable expenditures to their fast food and dessert expenditures equals which of the following?
(A) 3/20
(B) 1/5
(C) 1/3
(D) 3/8
(E) 3/5
(A) 3/20
(B) 1/5
(C) 1/3
(D) 3/8
(E) 3/5
13 Jul 2021, 13:30
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Bunuel
The overall spending did not change, and coffee was 5% of the budget. So if we double the spending on coffee, it is now 10% of the budget, which is 5% extra. We take that away from the fresh fruits and vegetables, originally 20% of the budget but now down to 15%.
The fast-food and dessert expenditure was always 100% - 5% - 50% = 45% of the budget, so the asked ratio is 15/45 = 1/3.
Ans: C
13 Jul 2021, 14:25
Kudos
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Hello
In problems like this it is helpful to use numbers that are easy to work with.
Let's say that the total budget was $100, this turns the percentages into dollar amounts that are easier to conceptualize and think about.
If 5% of the $100 budget was previously spent on coffee, the family used to spend $5 on coffee.
Similarly, the family used to spend 20% or $20 on fruits and vegetables.
To determine the percent and amount spent on fast food, add up the other percentages and subtract from 100.
5 + 20 + 30 = 55
100 - 55 = 45
45% or $45 was spent on fast food
We are told that the price of coffee doubled.
$5 x 2 = $10 is the new price of coffee
What is the additional coffee expense?
They used to spend $5 and now they spend $10 on coffee.
$10 - $5 = $5
$5 is the additional coffee expense that must now be subtracted from the fruit and vegetable budget to spend the same amount overall
The family used to spend $20 on fruits and vegetables
$20 - $5 = $15
The family now spends $15 on fruits and vegetables and $10 on coffee.
The amount spent on fast food has not changed and remains $45
The new ratio of fruits to fast food is therefore $15 : $45
To simplify, divide both sides by the same number
\(\\
\frac{15}{15}:\frac{45}{15} = 1:3\)
The ratio is 1:3 and the answer is (C)
In problems like this it is helpful to use numbers that are easy to work with.
Let's say that the total budget was $100, this turns the percentages into dollar amounts that are easier to conceptualize and think about.
If 5% of the $100 budget was previously spent on coffee, the family used to spend $5 on coffee.
Similarly, the family used to spend 20% or $20 on fruits and vegetables.
To determine the percent and amount spent on fast food, add up the other percentages and subtract from 100.
5 + 20 + 30 = 55
100 - 55 = 45
45% or $45 was spent on fast food
We are told that the price of coffee doubled.
$5 x 2 = $10 is the new price of coffee
What is the additional coffee expense?
They used to spend $5 and now they spend $10 on coffee.
$10 - $5 = $5
$5 is the additional coffee expense that must now be subtracted from the fruit and vegetable budget to spend the same amount overall
The family used to spend $20 on fruits and vegetables
$20 - $5 = $15
The family now spends $15 on fruits and vegetables and $10 on coffee.
The amount spent on fast food has not changed and remains $45
The new ratio of fruits to fast food is therefore $15 : $45
To simplify, divide both sides by the same number
\(\\
\frac{15}{15}:\frac{45}{15} = 1:3\)
The ratio is 1:3 and the answer is (C)
