Question

A bag contains 25 cents and 50 cent coins whose total value is $30 if the number of 25 cent coins is four times that of 50 cent coins, find the number of each type coins. please may I also have the equation.​

Answer 1

Explanation:

Let 25 cent coin be A and 50 cent coin be B

Given

Total value of 25 cents coin and 50cents coin is $30

That’s

25A + 50B = 30

Also, 25 cents coin is equal to four times that of 50

So,

A = 4B

We now have

25A + 50B = 30

A = 4B

Substitute 4B for A into the first equation

25(4B) + 50B = 30

25 x 4B + 50B = 30

100B + 50B = 30

150B = 30

Divide both sides by 150 to isolate B

150B/150 = 30/150

B = 1/5

Recall

A = 4B

Therefore

A = 4 x 1/5

= 4/5

Number of 25 cents coin is 4/5 and that of 50 cents coin is 1/5

Answer 2

Number of 25 cents coins is 80 and number of 50 cents coins is 20.

Explanation:

Given,

A bag contains of total value $ 30.

Number of 25 cent coins is four times that of 50 cent coins.

To find number of 25 cents coin is x

Number of 50 cents coin is y

According to the problem,

`(x)/(4) +(y)/(2) = 30` ----- eq 1

x = 4y------ eq 2

Now, we will solve these two equation.

Putting the values of x = 4y in eq 1 we get,

`(4y)/(4) +(y)/(2) = 30`

or,
`y +(y)/(2) = 30`

or,
`(3y)/(2)` = 30

or, y = 20

So, x = 4×20 = 80

Hence,

Number of 25 cents coins = 80 and number of 50 cents coins = 20