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**+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

#1**+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*90 = 48

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**+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

#6**+10 **

Best Answer

* 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