SOLUTION: I cannot understand this answer, please help. Thank you. Justin spent 3/10 of his money on 11 packs of cards. He would be able to buy another 29 such packs of cards with the rema

Question 1188270: I cannot understand this answer, please help. Thank you.
Justin spent 3/10 of his money on 11 packs of cards. He would be able to
buy another 29 such packs of cards with the remaining amount of his
money and an additional $20.
(a) What was the price of 1 pack of cards?
(b) How much money did Justin have at first?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you need to introduce 2 variables.
x is the total amount of his money.
c is the cost of one pack of cards.

he spent 3/10 of his money on 11 packs of cards.

3/10 of his money = 3/10 * x.
total cost for the cards = 11 * c.

equation is 3/10 * x = 11 * c.

with the rest of his money plus another 20 dollars, he could buy 29 more cards.

rest of his money is 7/10 * x + 10.
total cost for the cards is 29 * c.

equation is 7/10 * x + 20 = 29 * c.

you have two equations that need to be solved simultaneously.

they are:

3/10 * x = 11 * c.
7/10 * x + 20 = 29 * c

multiply both sides of the first equation by 7 and multiply both sides of the second equation by 3 to get:

21/10 * x = 77 * c
21/10 * x + 60 = 87 * c

subtract the first equation from the second to get:

60 = 10 * c

solve for c to get:

c = 60/10 = 6.

the cost of 1 pack of cards is 6 dollars.

now that you know the cost for 1 pack of cards, you can find out much money he had to start with.

3/10 * x = 11 * c = 11 * 6 = 66 dollars.

solve for x to get:

x = 66 * 10 / 3 = 220 dollars.

your soluion is that the cost of one pack of cards is 6 dollars and the total amount of money that he had to start with was 220 dollars.

i'm assuming dollars, but you can replace that with any other denomination that you are dealing with.

to confirm, replace the original equations with 220 for x and 6.00 for c.

3/10 * x = 11 * c becomes 3/10 * 220 = 11 * 6 which becomes 66 = 66.
7/10 * x + 20 = 29 * c becomes 7/10 * 220 + 20 = 29 * 6 which becomes 174 = 174.

both equations are confirmed to be good when x = 220 and c = 6.

your solution is:

he has 220 dollars to start with and the cost of one pack of cards was 6 dollars.

Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.
Justin spent 3/10 of his money on 11 packs of cards. He would be able to
buy another 29 such packs of cards with the remaining amount of his
money and an additional $20.
(a) What was the price of 1 pack of cards?
(b) How much money did Justin have at first?
~~~~~~~~~~~~~

Let x be the amount Justin had at first. He spent 0.3x to buy 11 packs of cards; hence, each pack costs dollars. After spending 3/10 of his money, he still have 0.7x of his money remainder. Next you write the equation as you read the problem 0.7x + 20 = . It is your basic equation to solve and to find x. To solve it, multiply both sides by 110. You will get 77x + 2200 = 29*3x 2200 = 29*3x - 77x 2200 = 10x x = 2200/10 = 220 dollars. So, Justin had 220 dollars, at first. 3/10 of 220 dollars is 3*22 = 66 dollars. Since Justin bought 11 packs of cards for 66 dollars, each pack of cards costs 66/11 = 6 dollars.

Solved.

-------------

So, you can easily solve the problem using only one single equation for one single unknown,
as if you knows NOTHING about systems of equations.

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