The cost of 10 oranges and 3 apples is $2.77. Twenty four oranges and 12 apples cost $8.04. How do you find cost of each orange and apple?

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Answer 1 · 2015-09-23T13:54:25

An apple costs #0.29#$, while an orange costs #0.19#$.

Let's call #a# the price of an apple and #o# the price of an orange.

From the first relation, we know that

#10o +3a=2.77#

From the second, we know that

#24 o + 12 a =8.04#

Now, there are several ways to solve this system: for example, we can multiply by #4# the first equation to get

#10o +3a=2.77 -> 40o + 12a = 11.08#

Now, subtracting the second equation from the first, we get

#40o + 12 a - 24o - 12a = 11.08-8.04#, which means

#16o = 3.04#, from which we get #o=3.04/16=0.19#

Once we know the price of an orange, we can easily get the price of an apple by sostituition: for example, from the first equation we know that

#10o +3a=2.77#

but now we know that an orange costs #0.19#, so this equation becomes

#1.9+3a=2.77#, from which we get

#a={2.77-1.9}/3=0.29#