Answer:
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.
