Matrices ?

Question

A collection of nickels, dimes, and quarters has a value of $3.40. There are twice as many dimes as quarters and there are 32 coins in all. How many of each kind are there ?

Answer 1

Let N=number of nickels    D= number of dimes     Q= number of quarters

 

From the first sentence: 5N + 10D + 25Q = 340  

 

From the second sentence: D = 2Q  

 

From the third sentence: N + D + Q = 32

 

Add the first equation and the second equation to lose N:

 

5N + 10D + 25Q =340

 N  +  D   + Q =32

 

Multiply the second equation by -5

 

5N + 10 D + 25Q = 340

-5N -5D -5Q = -160

 

5D +20Q = 180

 

Since D = 2Q, substitute 2Q for D so 5(2Q) + 20Q = 180

 

10Q + 20Q = 180

30Q= 180

so Q = 6

 

If D = 2Q then D =2(6) or 12

 

If N + D + Q =32, substitute 12 for D and 6 for Q

 

N + 12 + 6 =32

N +18 = 32

N = 14

 

Denny Rose 

Galion, OH