12 quarters and 7 dimes.
Work Step by Step
x=numbers of dimes, y=number of quarters. The total value of dimes and quarters is 370, so 10x+25y=370. The number of quarters is 5 coins more than dimes so y=x+5 Equations: 10x+25y=370, y=x+5. Use substitution to solve: 10x+25(x+5)=370 10x+25x+125=370 35x+125=370 35x=245 x=7 So the number of dimes is 7. y=x+5 y=7+5 y=12 So the number of quarters is 12 Check your work: 10(7)+25(12)=370 70+300=370 370=370 So the solutions are right, and there are 7 dimes and 12 quarters.