+0

# Percentage

0
603
7

On monday, Tanya counted the number of 10-cent coins, 20-cent coins and 50-cent coins in her piggy bank. The number of 10-cent coins was 24 more than the number of 50-cent coins. On tuesday, Tanya spent 3 over

5 of the 10-cent coins, 1 over 4 of the 20-cent coins and 18 50-cent coins. Tanya then found that she had an equal number of 10-cent coins and 20-cent coins. The number of 50-cent coin now formed 40% of all the coins she had left.

(a)Tanya had how many 10-cent coins at first?

(b)How much money did Tanya spent in all?

Guest Apr 30, 2015

#6
+85759
+10

Addendum......I believe I spotted Melody's error

She has

0.72X  -  16.8 =X  - 42

16.8 + 42  =  x - 0.72X

But the 16.8 should be negative

So....it should be....

-16.8 + 42  = 0.28X

25.2  = 0.28X

X = 90  = the number of 10 cent coins, originally.....

And our answers would now agree....

Hey.....no biggie......!!!!

CPhill  May 2, 2015
Sort:

#1
+92221
+5

On monday, Tanya counted the number of 10-cent coins, 20-cent coins and 50-cent coins in her piggy bank. The number of 10-cent coins was 24 more than the number of 50-cent coins. On tuesday, Tanya spent 3 over

5 of the 10-cent coins, 1 over 4 of the 20-cent coins and 18 50-cent coins. Tanya then found that she had an equal number of 10-cent coins and 20-cent coins. The number of 50-cent coin now formed 40% of all the coins she had left.

(a)Tanya had how many 10-cent coins at first?

This one is really confusing is it not :)

Let the number of tens be X, the number of twenties be Y and the number of fifties be Z

Z+24=X

X-24=Z

-----

now after her spending spree this is what what she has left

(2/5)X+(3/4)y+(Z-18)   coins

and

(2/5)X=(3/4)Y

so Y = 0.4X/0.75 = (8/15)X      and from before       X-24=Z

also

0.4((2/5)X+(3/4)y+(Z-18) )=Z-18

The first thing we want is X so I will get all this in terms of X and solve and hopefully the answer is a whole number. :)

0.4((2*(2/5)X+(X-24-18))=X-24-18

0.4((0.8X+(X-42))=X-42

0.4(1.8X-42)=X-42

0.4*1.8X   -   0.4*42=X-42

0.72X  -  16.8 =X  - 42

-16.8+42 =X  - 0.72X

25.2=0.28X

X=90

so there was originally 90 ten cent peices

(b)How much money did Tanya spent in all?

X=90

Y=(8/15)X = 8/15*9048

She spent    (3/5)*X = (3/5)*90 = 54 ten cent coins = \$5.40

She spent    (1/4)*Y = 0.25*48 = 12 twenty cent coins = \$2.40

She spent   18 fifty cent coins  =  \$9

Total spent = 5.40+2.40+9= \$16.80

I fixed this after CPhill told me, by Private message,  of a careless error.    Thanks Chris

I only just realized that he has posted a proper answer underneath then whited it out.

You don't need to do that Chris - I shall unwhite it.  It is a good answer :)

Melody  Apr 30, 2015
#3
+85759
+10

I get a different answer from Melody on this one.....

Let x  be the number of 50 cent coins in the beginning

Let y be the number of 20 cent coins in the beginning

Let x + 24 be the number of 10 cent coins in the beginning

And after the spree we have

x - 18   = the number of 50 cent coins

(2/5)(x + 24) = the number of 10 cent coins = the number of 20 cent coins

So the total coins left after the spree = 2(2/5)(x + 24) + ( x -18)  = (4/5)(x + 24) + (x - 18)

And 40% of these = the number of 50 cent coins left   ....  so we have

.40[ (4/5)(x + 24) + (x - 18) ] = (x - 18)

(2/5)[ (4/5 (x + 24) + (x - 18) ] = (x - 18)

[ (4/5 (x + 24) + (x - 18) ]  = (5/2)(x - 18)   multiply through by 10

8(x + 24) + 10( x - 18) = 25(x - 18)

8x + 192 + 10x - 180  = 25 x - 450   simplify

18x + 12  = 25x - 450

462 = 7x    divide by 7 on each side

x = 66  this is the number of 50 cent coins in the beginning

And x + 24 = (66 + 24) = 90 were 10 cent coins in the beginning

And notice that (3/4)y = (2/5) (x + 24)...  so y = (8/15)(66 + 24) = (8/15)(90) = 48 coins

So....there were 48 20 cent coins originally

Now.....let's check the math....

The total number of coins after the spree =

[(4/5)(66 + 24) + (66 - 18) ]  = 120

And (66 - 18) = 48 of these were 50 cent coins

So..... 48 / 120 = 40% were 50 cent coins

And after the spree....there were an equal number of 10 and 20 cent coins.....check ...(2/5)(90) = (3/4)(48) = 36 each

So the total spent  = (3/5)(90)(.10) + (1/4)(48)(.20) + (18)(.50)  = \$16.80

I believe Melody has a slight error

She gets 210 10 cent  coins at the start    .....and 2/5 of these are left = 84 left

And this is equal  to the number of 20 cent coins left

And she calculates the number of 50 cent coins left = 210 - 42 =  168

So....the total coins left = [ 84 + 84 + 168]  = 336 coins left

But 168 / 336 = 50% of the coins left are 50 cent coins......and this is too much

Can anyone reconcile these differences ???

CPhill  May 2, 2015
#4
+26640
+10

Here's my check:

This supports Chris's results.

.

Alan  May 2, 2015
#5
+85759
+10

Thanks, Alan.....!!!

CPhill  May 2, 2015
#6
+85759
+10

Addendum......I believe I spotted Melody's error

She has

0.72X  -  16.8 =X  - 42

16.8 + 42  =  x - 0.72X

But the 16.8 should be negative

So....it should be....

-16.8 + 42  = 0.28X

25.2  = 0.28X

X = 90  = the number of 10 cent coins, originally.....

And our answers would now agree....

Hey.....no biggie......!!!!

CPhill  May 2, 2015
#7
+92221
+5

WOW Everyone's answers got white.  You didn't need to do that - I am a big girl   LOL

I have unwhited the whole thread  :)

Thanks Alan and Chris  :)    Three heads are always better than one    (especially when the one is mine lol)

Melody  May 3, 2015

### 26 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details