Mrs Robinson bought some chocolates and lollipops in the ratio 7:4.The price of all thechocolates to the price of all the lollipopswas in the ratio 5:2.She spent $ 127.40 in all.If each lollipop costs 15 cents less than each chocolate,how many lollipops did she buy?

Answer :

 
Ratio of price of all the chocolates and lollipops is=5:2
 
Let k is the proportion value
 
Then :
 
5k + 2k = 12740 cents

$\Rightarrow$k=1820
 
Hence
price for all the chocolates =5k=9100 cents
price for  all the lollipops = 2k=3640 cents
 
given:
 
ration to the no of chocolates and lollipops is 7:4
 
let proportion value = x
total no if chocolates =7x
total no of lollipops = 4x
also given
 
Let price of each chocolate = p
price of each lollipop = price of each chocolates -15
 = p - 15
 
From the question:
 
Total no of chocolates $\times$ price for each chocolates =9100

7x $\times$ p = 9100                  ----1

Total no of lollipops $\times$40 price for each lollipop=36.4

4x $\times$ ( p - 15 ) = 3640       ----2
 
Divide equation 2 from 1 , and get
 
$\frac{4 \left( p-15 \right)}{7p} = \frac{3640}{9100}$

$\Rightarrow$ p = 50 cents
 
Substitute that value in equation 1 , we get 
 
7x $\times$50 = 9100
$\Rightarrow$x  =  26
 
Total no of lollipops = 4 $\times$ 26  = 104                           ( Ans )