work out the total value of coins in the bag

bumblebee123

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question:

a bag contains 2p coins, 5p coins and 10p coins only. The ratio of the number of 2p coins to the number of 5p coins to the number of 10p coins in the bag is

2 : 4 : 7 the total value of the 10p coins is £10 more than the total value of 5p coins. work out the total value of coins in the bag

any help would be really appreciated!
 
question:

a bag contains 2p coins, 5p coins and 10p coins only. The ratio of the number of 2p coins to the number of 5p coins to the number of 10p coins in the bag is

2 : 4 : 7 the total value of the 10p coins is £10 more than the total value of 5p coins. work out the total value of coins in the bag

any help would be really appreciated!
Start with defining "find"s:

# of 10p coins = T

# of 5p coins = F

# of 2p coins = W

Given:

The ratio of the number of 2p coins to the number of 5p coins to the number of 10p coins in the bag is 2 : 4 : 7

So:

W/T = 2/7...................................................(1)

and

W/F = 2/4...................................................(2)

Set up a third equation with the other given (the total value of the 10p coins is £10 more than the total value of 5p coins)

Now you will have 3 equations and 3 unknowns - solve it.
 
sorry this makes no sense ?

Using Subhotosh's variables:

T : F : W = 2 : 4 : 7
You need to find T, F and W ie 3 variables so you need 3 equations

If we pull this ratio apart we get
T : W = 2 : 7
ie \(\displaystyle \frac{T}{W}=\frac{2}{7}\)
ie \(\displaystyle T = \frac{2}{7}*W\) ……… (1)

Do the same with F : W to get F in terms of W. That will give you equation (2).

Equation (3) will come from "the total value of the 10p coins is £10 more than the total value of 5p coins".

If there are W 10p coins then the total value of those coins is 10*W pence.
If there are F 5p coins then the total value of those coins is ??? pence. (You can do that)

Now form an equation from the statement "the total value of the 10p coins is £10 more than the total value of 5p coins". Be careful and change the pounds into pence first.

Now tell us your three equations.
 
sorry this makes no sense ?
Hello bumblebee123. Let's discuss each thing that confuses you. What is the very first part in the replies that makes no sense for you?

If you can, please explain why that part is confusing. That is, tell us your thoughts, if you're unable to try any work. We'll go from there.

Also, if you've not solved systems of equations with multiple variables, let us know if you need help finding links to lessons and worked examples.

Cheers ?
 
(1) T = 2/7 * W

(2) F = 4/7 * W

(3) The total value of coins if there a F 5p coins = 5*F pence
 
I think I've done it!

# of 10p coins = T

# of 5p coins = F

# of 2p coins = W

F/W = 4/7

F = 4/7 * W

10W = 1000p +5F

10W = 1000p + 5(4/7 * W )

10W = 1000p +20/7W

50/7W = 1000p

W = 140

so there are 140 ten pence coins

7 parts = 140 coins

1 part = 20 coins

there are ( 2*20 ) 40 two pence coins ( = 80p )

80 five pence coins (4*20 ) ( = 400p )

and 140 ten pence coins (7*20 ) ( = 1400p )

total value of coins: 80p + 400p + 1440p = 18880p = £18.80p
 
total value of coins: 80p + 400p + 1440p = 18880p = £18.80p
Your post is too "headachy" to comment on....
If wrapped-up "carefully!"; you'll you'll get:
40 2pence : .80
80 5pence : 4.00
140 10pence : 14.00
That's 260 coins = 18.80 pounds

You ended up with same...but confusingly...
 
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