Question

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 1

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 )