Problema Solution
Roshni has 30 coins in her backpack, all nickels, dimes, and quarters. She has a total of $4.30. If Roshni has 5 more dimes than nickels, how many quarters does she have,
Answer provided by our tutors
Let the number of nickels, dimes and quarters be x, y and z respectively
x+y+z= 30
She has 5 more dimes than nickels
=> y=x+5
Using x+y+z =30:
z= 30-y-x
=> z= 30- (x+5) -x
=> z= 25-2x
Now, sum of all coins =4.30
0.05x+ 0.10y + 0.25z= 4.30
=> 0.05x + 0.10 ( x+5 ) + 0.25 ( 25-2x )= 4.30
0.05x +0.10x + 0.5 + 6.25 -0.5x= 4.30
=> 6.25 + 0.5 -4.30 = 0.5x - 0.05x - 0.10x
=> 2.45= 0.35x
=> x= 2.45/ 0.35 = 7
=> y= 12
=> z= 11