SOLUTION: Hi can someone help with the below mentioned problem. Ahmad had 46 more $5 notes than $10 notes in his piggy bank. he took out some $ 5 notes. the total amount of $5 notes he too

Question 1140649: Hi can someone help with the below mentioned problem.
Ahmad had 46 more $5 notes than $10 notes in his piggy bank. he took out some $ 5 notes. the total amount of $5 notes he took out was $545. in the end, he had 8 times as many $10 notes as $5 notes.
a) How many $5 notes did ahmad have at first?
b) How much money did Ahmad have left in his piggy bank?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of 5 dollar notes.
y = number of 10 dollar notes.

ahmad has 46 more five dollar notes than ten dollar notes.

equation for that is x = y + 46

he takes out 545 dollars in five dollar notes.

545 / 5 = 109 five dollar notes that he took out.

in the end he had 8 times as many ten dollar notes as five dollar notes.

the equation for that is y = 8 * (x - 109)

you have two equations that need to be solved simultaneously.

they are:

x = y + 46
y = 8 * (x - 109)

in the first equation, solve for y to get y = x - 46

your two equations are now:

y = x - 46
y = 8 * (x - 109)

replace y with x - 46 in the second equation to get:

x - 46 = 8 * (x - 109)

simplify to get x - 46 = 8 * x - 872

subtract x from both sides of the equation and add 872 to both sides of the equation to get:

872 - 46 = 8 * x - 1

simplify to get 826 = 7 * x

solve for x to get x = 118

since y = x - 46, then y = 118 - 46 = 72

you have x = 118 and y = 72

x is the number of five dollar notes.
y s the number of ten dollar notes.

to begin with, he had 118 five dollar notes and 72 ten dollar notes.

that would make a total of 118 * 5 + 72 * 10 = 1310 dollars.

he took out 545 dollars, so he was left with 1310 - 545 = 765 dollars.

he started with 118 five dollars notess and 72 10 dollar notes.

he took out 109 five dollar notes, so he was left with 9 five dollar notes and 72 ten dollar notes.

the total money he was left with was 9 * 5 + 72 * 10 = 765 dollars.

numbers check out so the solution looks good.

the solution is:

ahmad has 118 five dollar notess to start with.

ahmad has 765 dollars left in his piggy bank.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

He started with 46 more $5 notes than $10 notes.

He took out $545 in $5 notes; that is 545/5 = 109 $5 notes.

So then he had 109-46 = 63 FEWER $5 notes than $10 notes.

At that point he had 8 times as many $10 notes as $5 notes.

You might be able to solve the problem mentally from there....

Or use algebra:

Let x = number of $5 notes left
Then 8x = number of $10 notes

The number of $5 notes is now 63 less than the number of $10 notes:

Easily solved with basic algebra.

Then, knowing the numbers of $5 and $10 notes at the end, you can easily answer both of the given questions.
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