Problem Solving

boomgoesthegmat wrote:In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:2:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?

A) 900
B) 720
C) 675
D) 450
E) 225

OA: D

GIVEN: household expenses $ : food $ : miscellaneous $ = 5:2:1
5 + 2 + 1 = 8.
So, for every $8 in the budget, $5 goes to household expenses, $2 goes to food and $1 goes to miscellaneous

$1800/8 = $225

So...
- household expenses = 5($225) = $1225
- food = 2($225) = $450
- miscellaneous = 1($225) = $225

Answer: D

RELATED RESOURCE: This video explains the technique for dividing amounts into specific ratios (as we did with this question): https://www.gmatprepnow.com/module/gmat ... video/1081

Cheers,
Brent

boomgoesthegmat wrote:In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:2:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?

A) 900
B) 720
C) 675
D) 450
E) 225

OA: D

To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:

Household Expenses : Food : Miscellaneous = 5x : 2x : x

Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:

5x + 2x + x = 1,800

8x = 1,800

x = 225

Thus, the total amount allocated to food is 2 x 225 = $450.

Answer D

Hi All,

We're told that in the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:2:1, respectively and that the total amount allocated to these three categories is $1,800. We're asked for the amount allocated to food. This is a standard ratio question and the 'math' behind it can be done in a variety of ways (depending on how you "see" the relationships involved).

To start, with a ratio of 5:2:1, it's highly likely that....
The amount spent on household expenses is a multiple of $5
The amount spent on food is a multiple of $2
The amount spent on miscellaneous items is a multiple of $1
The TOTAL spent will be a multiple of $5+$2+1 = $8

This means that for every $8 that is spent $2 will be on food. $2/$8 = 1/4, so 1/4 of the $1800 total will be spent on food.

(1/4)($1800) = $450

Final Answer: D

GMAT assassins aren't born, they're made,
Rich