SOLUTION: Hi Mrs Robinson bought some chocolates and lollipops in the ratio of 7 to 4. The price of all the chocolates to the price of all the lollipops was in the ratio of 5 to 2. If each

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Question 1207183: Hi
Mrs Robinson bought some chocolates and lollipops in the ratio of 7 to 4. The price of all the chocolates to the price of all the lollipops was in the ratio of 5 to 2. If each lollipop cost 15c less than each chocolate how many lollipops did she buy.
Thanks
Found 3 solutions by greenestamps, ikleyn, josgarithmetic:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the cost in cents of each lollipop
Then x+15 is the cost in cents of each chocolate

Since the chocolates and lollipops were in the ratio 7:4, the ratio of the costs of the chocolates to the cost of the lollipops was %287%28x%2B15%29%29%2F%284%28x%29%29.

That ratio of costs was 5:2

%287%28x%2B15%29%29%2F%284%28x%29%29=5%2F2
14%28x%2B15%29=20%28x%29
14x%2B210=20x
6x=210
x=35

From the given information, we know...
cost of each lollipop: x = 35 cents
cost of each chocolate: x+15 = 50 cents

But the question asks us to find the number of lollipops she bought -- and there is no information given that allows us to answer that question. We only know that the chocolates and lollipops were in the ratio 7:4. So, for example...

7 chocolates and 4 lollipops
cost of chocolates 7(50) = 350, cost of lollipops 4(35) = 140, ratio of costs 350:140 = 5:2

35 chocolates and 20 lollipops
cost of chocolates 35(50) = 1750, cost of lollipops 20(35) = 700, ratio of costs 1750:700 = 5:2

etc....

Another problem (from the same student maybe) for which we can't find the answer....

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

I agree with @greenestamps that the problem,  as it is posed,  can not be answered.

To it,  I would add that wording in the problem is perpendicular to the meaning of words.

Thus,  the problem says  " The price of all the chocolates . . . ".

This fragment is incorrect,  since the term  " price "  relates to single item/(single piece of chocolate).
It can not be used in this combination  " price of all the chocolates . . . "

The same notice is to the fragment  " the price of all the lollipops . . . "

For  Math problems,  it is not the same which word/words to use . . .


As a conclusion,  this problem does not fit for any reasonable purpose.


It is good only to scare people around.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This sentence is troubling:
The price of all the chocolates to the price of all the lollipops was in the ratio of 5 to 2.

One might have to assume you really mean, "cost" and not "price".
                   PRICE(cents)     AMOUNT          COSTS

CHOCOLATES          5y/(7x)           7x             5y

LOLLIPOPS           2y/(4x)           4x             2y

DIFFERENCE           15

One useful equation would be %285y%29%2F%287x%29-y%2F%282x%29=15

Maybe want to change the form using 14x;

10y-7y=210x

3y=210x

y=70x--------------Can you find some whole numbered solution? More than one solution, as whole numbers?

Something still seems off here.