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Quart-Gallon Question [#permalink]
24 Dec 2007, 17:13

Here is a question which can become trickier depending upon your interpretation:

At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon and Brand Y motor oil is sold by the quart. Excluding sales tax, what is the total cost for 1 gallon of Brand X antifreeze and 1 quart of Brand Y motor oil?

(1). Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10 quarts of Brand Y motor oil is 58. (There is no quantity discount.)

(2). Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12 quarts of Brand Y motor oil is 44. (There is no quantity discount.)

Each statement on it's own leaves itself open to an almost infinite number of possible prices for X and Y. Only by combining them do we get our 2 equations for 2 variables. Normally you would want to answer C and move on, but we can do the math here to show it.

6x+10y=58
4x+12y=44

combine them:

2x-2y=14
2x=2y+14
x=y+7

plug it back in

6(y+7)+10y=58
6y+42+10y=58
16y=16
y=1

plug that back in

4x+12(1)=44
4x=32
x=8

so now plug 1 and 8 in to make sure they work

6(8)+10(1)=58
48+10=58
58=58 checks out

4(8)+12(1)=44
32+12=44
44=44 checks out

and there's your answer. 1 gallon of X and 1 quart of Y = $9

you don't need to convert quarts to gallons for this question, because the base/unit prices of the liquids are not the same. Just think of buying tables and chairs, you don't pay for them per volume of wood.