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Carrots sell for $2.10 per pound, and crackers sell for $2.90 per pound. Glen bought some carrots and some crackers. The total weight was 2.3 pounds and cost $6.03.

How many pounds of carrots and how many pounds of crackers did Glen buy?  A.0.5 pounds of carrots; 1.8 pounds of crackers  B.0.8 pounds of carrots; 1.5 pounds of crackers  C.1 pound of carrots; 1.3 pounds of crackers  D.1.5 pounds of carrots; 0.8 pound of crackers



Answer :

SparklesInInk
You can solve this problem by adding/subtracting expressions.

You have two expressions here: x + y = 2.3 and 2.1x + 2.9y = 6.03

The goal is to get rid of one of the variables because when there are two variables it's pretty impossible to figure them out when you don't know either. To do this you need to add or subtract the expressions. To do that you need to make one of the variables the same in both expressions.

Let's make the x's the same. So in one problem you have x and in the other you have 2.1x. You want to multiply the x by 2.1 so they are both 2.1 x. To do that you have to multiply the whole expression by 2.1 which would be 2.1(x + y) = 2.3(2.1) which equals 2.1x + 2.1y = 4.83.

Now you have two expression 2.1x + 2.1y = 4.83 and 2.1x + 2.9y = 6.03. Change the first one to all negatives to subtract it. 2.1x + 2.1y = 4.83 becomes -2.1x - 2.1y = -4.83. Now you can subtract the expression like this.

2.1x + 2.9y = 6.03
-2.1x - 2.1y = -4.3
________________
 0x   + 0.8y = 1.2 or 0.8y = 1.2 (Hooray the x is gone!)

Now you just finish solving it. 

0.8y = 1.2
y = 1.2/0.8
y = 1.5

y represented the crackers so whatever answer has 1.5 crackers is the correct one

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