Question

Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.

Answer 1

Given :

Jason has dimes and quarters of  worth $2.25

The number of dimes = twice number of quarters

To Find :

The number of dimes and the number of quarters that Jason has

Solution :

Let The number of dimes that Jason has = d

Let The number of quarters that Jason has = q

According to question

number of dimes = 2× number of quarters

i.e                      d = 2 q                      ...............1

∵  1 dime = $0.10

And 1 quarter = $0.25

So,  The equation can be written as    

               $0.10 × d + $0.25 × q = $2.25

Or,          $\dfrac{10}{100}$ × d + $\dfrac{25}{100}$  × q = $\dfrac{225}{100}$

Taking  $\dfrac{1}{100}$  as common

Or,          10 d + 25 q = 225

Or,            2 d + 5 q = 45

From eq 1

              2 × 2 q + 5 × q = 45  

i.e           4 q + 5 q = 45

Or,                   9 q = 45

∴                          q = $\dfrac{45}{9}$

i.e ,                       q = 5

So, The number of quarters = q = 5

Put the value of q into eq 1

∵            d = 2 × q

So,        d = 2 × 5

i.e          d = 10

So, The number of dimes = d = 10

Hence, The number of quarters is 5   And  The number of dimes is 10   Answer

Answer 2

Answer:

Quarters: 5 and Dimes: 10