Question 1210397
<br>
There are many ways you could set up this problem for solving.  I looked briefly at a few different ways before choosing a method that looked as if it would be relatively easy.  I would hope that other tutors might come to you with different solutions.<br>
He spent a total of $61.20; and he spent $22.80 more for the apples than for the pears.<br>
let a = cost of the apples
let p = cost of the pears<br>
{{{a+p=61.20}}}  the total cost was $61.20
{{{a-p=22.80}}}  the cost of the apples was $22.80 more than the cost of the pears<br>
Solve the pair of equations by adding the two equations to solve for a and then use that number to find p.<br>
{{{2a=84.00}}}
{{{a=42.00}}}
{{{p=42.00-22.80=19.20}}}<br>
The total cost of the apples was $42; the total cost of the pears was $19.20.<br>
The ratio of the number of apples to the number of pears was 7:4.  So<br>
let 7x = number of apples
then 4x = number of pears<br>
Find the cost of x apples and the cost of x pears:<br>
{{{7x=42}}}
{{{x=6}}}
The cost of x apples is $6.<br>
{{{4x=19.20}}}
{{{x=4.80}}}
The cost of x pears is $4.80.<br>
The cost of x apples is $6 - $4.80 = $1.20 more than the cost of x pears.  Each apple costs $0.30 more than each pear, so x = $1.20/$0.30 = 4.<br>
The cost of x=4 apples is $6, so the cost of each apple is $6/4 = $1.50.<br>
The cost of x=4 pears is $4.80, so the cost of each pear is $4.80/4 = $1.20.<br>
Check the results we have with the original given information:<br>
He bought 7x = 28 apples at $1.50 each for a total of 28($1.50) = $42.00.
He bought 4x = 16 pears at $1.20 each for a total of 16($1.20) = $19.20.
The total he spent was $42.00+$19.20 = $61.20.<br>
Looks good.  Now answer the questions that were asked.<br>
(a) How much did he spend on the pears?
ANSWER: $19.20<br>
(b) How many pears did he buy?
ANSWER: 16<br>