Tom and barb have only nickels and dimes. barb has 75 cents and tom has 90 cents. both have the same number of coins and tom has the same number of dimes as barb has nickels. how many nickels does barb have?

Barb have 4 nickels.

Step-by-step explanation:

Tom and Barb have nickels and dimes only.

Let numbers of nickels and dimes Tom have = n and d

Let numbers of nickels and dimes Barb have = n' and d'

Both have same number of coins then equation will be  

n + d = n' + d' (1)

Tom has same number of dimes as Barb has nickels

d = n'

By replacing d = n' in equation (1)

n + n' = n' + d'

n = d'

It has been given in the question that Barb has 75 cents and Tom has 90 cents in the form of nickels and dimes.

0.05n + 0.10d = 0.75

Dividing this equation by 0.05

n + 2d = 15(2)

0.05n' + 0.10d' = 0.90

By diving this equation by 0.05

n' + 2d' = 18

Since n' = d and d' = n

Then d + 2n = 18 (3)

Now we multiply equation (2) by 2 and subtract it by equation (3)

2(n + 2d) - (d + 2n) = 15×2 - 18

2n + 4d - d - 2n = 30 - 18

3d = 12

d = 4

Since d = n'

So n' = 4

Therefore, Barb have 4 nickels.

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