Last Updated on May 3, 2023
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
Answer: B
