How many coins of each type were there?

Question

Weir and Max put $75 in quarters and dimes in the box. There were 400 more dimes than quarters. How many coins of each type were there?  

Answer 1

assume number of quarters = x quarters

value of quarters in cents = 25x cents

assume number of dimes = y dimes

value of dimes in cents = 10y cents

equation 1 

25x + 10y = 7500

equation 2

y = x + 400

 

solve two equations in two unknowns x & y

 

25x + 10(x + 400) = 7500

25x + 10x + 4000 = 7500

35x = 7500 - 4000 = 3500

x = 3500/35 = 100 quarters

y = x + 400 = 500 dimes

 

check:

100 quarters = 2500 cents = $25

500 dimes = 5000 cents = $50

total = $75

 

all the best