Question 1210397
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Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4. He spent $61.20. He paid $22.80 more for the apples than the pears. Each apple was $0.30 more than each pears.
(a) How much did he spend on the pears?
(b) How many pears did he buy?

Let multiplicative factor be x
As ratio of apples to pears is 7:4, number of apples and pears purchased = 7x and 4x, respectively

Let amount spent on pears be p
Since $22.80 more was spent on apples than pears, then amount spent on apples = p + $22.80
A total of $61.20 was spent, so we then have: p + p + 22.8 = 61.2
                                                        2p = 61.2 - 22.8
                                                        2p = 38.4
                        <font color = red><font size = 4><b>p, or amount spent on pears</font></font></b> = {{{highlight_green(38.4/2 = highlight("$19.20"))}}} 

Since $19.20 was spent on “4x” pears, then cost of each pear = {{{19.2/(4x) = 4.8/x}}}
As $19.20 was spent on pears, $61.20 - $19.20, or $42 was spent on “7x” apples, and so, each apple cost {{{42/(7x) = 6/x}}}
Now, since each apple was $0.30 more than each pear, we get: {{{6/x = .3 + 4.8/x}}}  
                                                             6 = .3x + 4.8 ---- Multiplying by LCD, x 
                                                       6 - 4.8 = .3x
                                                           1.2 = .3x                                                             
                            x, or multiplicative factor = {{{1.2/.3 = 12/3 =  4}}}

<font color = magenta><font size = 4><b>Number of pears purchased:</font></font></b> 4x = 4(4) = <font color = magenta><font size = 4><b>16</font></font></b></pre>