# A certain fruit stand sold apples for \$0.70…

## Solution:

We are given that apples were sold for \$0.70 each and that bananas were sold for \$0.50 each. We can set up variables for the quantity of apples sold and the quantity of bananas sold.

b = quantity of bananas sold

a = quantity of apples sold

With these variables, it follows that:

0.7a + 0.5b = 6.3

We can multiply this equation by 10 to get:

7a + 5b = 63

You may now notice that we do not have any other information to set up a second equation as we sometimes do for problems with two variables. So, we must use what we have. Keep in mind that variables a and b MUST be positive whole numbers, because you can’t purchase 1.4 apples, for example. You also may notice that “7” and “63” have a factor of 7 in common. Thus, we can move “5b” to the other side of the equation and scrutinize the new equation carefully:

5b = 63 – 7a

5b = 7(9 – a)

b = [7(9 – a)]/5

Remember that a and b MUST be positive whole numbers here. Thus, 5 must evenly divide into 7(9 – a). Since we know that 5 DOES NOT divide evenly into 7, it MUST divide evenly into (9 – a). We can ask the question: What must a equal so that 5 divides into 9 – a? The only value a can be is 4. And we can check this:

(9 – a)/5 = ?

(9 – 4)/5 = ?

5/5 = 1

Since we know a = 4, we can use that to determine the value for b.

b = [7(9 – 4)]/5

b = [7(5)]/5

b = 35/5

b = 7

Thus a + b = 4 + 7 = 11