How many dimes and how many quarters

Question

jacks collection of dimes and quarters is worth $14.30. the number of dimes is 1 less than 2 times the number of quarters. How many dimes and how many quarters dlied he have? 

Answer 1

Let

no. of dimes =d 
no. of quarters =q

Write an equation for each statement


jacks collection of dimes and quarters is worth $14.30.
0 .10d + 0.25q = 14.30   ___________eq 1

the number of dimes is 1 less than 2 times the number of quarters.

 

d=2q-1                        ____________eq 2

 

subsitute value of d in eq 1

 

0 .10d + 0.25q = 14.30

0.10(2q-1) + 0.25q = 14.30

 

0.20q-0.10+0.25q = 14.30

 

0.45q -0.10 =14.30

 

0.45q =14.40

 

q = 32

 

d=2q-1=2(32)-1=64-1=63

 

no. of dimes =d  = 63
no. of quarters =q =32