Answer: Apples $0.18 (18 Cents) Bananas $0.14 (14 cents)
Explanation:
Math knowledge would give the cost for each item. We have:
4 apples + 6 bananas = $1.56
and
9 apples + 7 bananas = $2.60
To find a cost, we encode an apple as 'a', and a banana as 'b' in the following two main equations:
4a+6b=1.56
9a+7b=2.6
The following formula represents the situation by using elimination method to find, let's say, the banana value:
4a+6b=1.56 , 9a+7b=2.6
9×4a+9×6b=9×1.56, 4×9a+4×7b=4×2.6
36a+54b=14.04, 36a+28b=10.4
36a−36a+54b−28b=14.04−10.4
54b−28b=14.04−10.4
26b=14.04−10.4
26b=3.64
b=3.64÷26
b=0.14
That is a banana costs $0.14 (14¢).
Now we have found the value of a banana, we substitute this new value in one of the main equations above to reduce variables so that we can find the value of an apple as follows:
4a+6b=1.56
4a+(6×0.14)=1.56
4a+0.84=1.56
4a=1.56-0.84
4a=0.72
a=0.72÷4
a=0.18
Simply enough, an apple costs $0.18 (18¢), and a banana costs $0.14 (14¢).