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Question 1184348: Rita had some money. She spent 1/4 of her money on 9 notebooks and
9 pens. The cost of each notebook is 3 times the cost of each pen. Then,
she decided to buy some more notebooks with 5/8 of her original sum of
money. How many notebooks did Rita buy altogether?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the original amount of money she had is equal to x.
she bought 9 notebooks and 9 pens for 1/4 * x.
each notebook cost 3 times as much as each pen.
your equation is 9n + 9p = 1/4 * x.
since n = 3p, then replace n with 3p to get:
9 * 3p + 9p = 1/4 * x
simplify to get:
27p + 9p = 1/4 * x
combine like terms to get:
36p = 1/4 * x
solve for p to get:
p = 1/(4*36) * x
simplify to get:
p = 1/144 * x
since n = 3p, then n = 3/144 * x
she then spent 5/8 of her original money to buy more notebooks.
take 5/8 * x and divide it by (3/144) to get:
5/8 * x * 144/3 = 30 additional notebooks.
your solution should be that she bought 39 notebooks in total.
to see if this makes sense, i assumed x is equal to 900 dollars.
i could have chosen any amount and i would have gotten the same results, as you'll see below when i used 900.
she took 1/4 * 900 and bought 9 notebooks and 9 pens.
1/4 * 900 = 225.
n = price of one notebook.
p = price of one pen.
your equation is 9n + 9p = 225.
since n = 3p, then you get:
27p + 9p = 225.
combine like terms to get:
36p = 225.
solve for p to get:
p = 225/36 = 6.25.
since n = 3p, you get:
n = 3 * 6.25 = 18.75
the price of one notebook is 18.75 and the price of one pen is 6.25, if the total amount of money she had was assumed to be 900.
9n + 9p = 9 * 18.75 + 9 * 6.25 = 225, so it looks like the prices are right.
she then spent 5/8 * 900 on additional notebooks.
since each notebook costs 18.75, the bought 5/8 * 900 / 18.75 notebooks.
5/8 * 900 = 562.5
562.5 / 18.75 = 30.
she bought 30 additional notebooks for a total of 39.
the solution is confirmed to be good when we replace x with a real amount of mo ney.
your solution is that she bought 39 notebooks in total.
you get the same answer whether you works it with x or you work it with a real number to replace x with.
you still don't know what the value of x is, but assuming it is any real number should get you the same answer, as i got when i assumed it was 900.
the total amount of money she spent is 1/4 * 900 + 5/8 * 900 = 787.5.
with that money she bought 39 notebooks and 9 pens.
total amount she paid was 39 * 18.75 + 9 * 6.25 = 787.5
it all checks out, so i'm reasonably confident that the answer is correct.
Answer by MathTherapy(10549)  (Show Source):
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