Respuesta :
Answer:
[tex] N = 10, D= 2, Q=3[/tex]
Step-by-step explanation:
Notation
N= represent the number of nickels
D= represent the number of dimes
Q= represent the number of quarters
Solution to the problem
For this case we assume that a nickels represent 5 cents, a dime 10 cents and a quarter 25 cents. We know that the total ofor the 15 coins it's 1.45 or 145 cents. So we can set up the following equations:
[tex] N+D+Q= 15[/tex] (1)
[tex] 5N +10D + 25Q = 145[/tex] (2)
[tex] Q= \frac{N+D}{4}[/tex] (3)
The condition (3) is obtained from the statement "the number of quarters is 1/4 the number of nickels and dimes combined"
So on this case we have a linear system of 3 equation with 3 values unknown so then this system can be solved.
We can use substitution in order to solve the values.
We can rewrite the quation (3) on this way [tex]4Q= N+D[/tex]
And if we replace this into equation (1) we got:
[tex] 4Q + Q = 15[/tex]
[tex] Q =3[/tex]
And know we can use the following two equations:
[tex] N+D = 12[/tex] (1)
[tex] 5N + 10D = 70[/tex] (2)
If we solve N from equation (1) we got:
[tex] N = 12-D[/tex] and if we replace this into equation (2) we got:
[tex] 5(12-D) + 10 D = 70[/tex]
[tex] 60 -5D + 10D = 70[/tex]
[tex] 5D = 10 [/tex]
[tex] D= 2[/tex]
And then we can solve for N like this:
[tex] N = 12-D= 12-2 = 10[/tex]
So then our final solution would be:
[tex] N = 10, D= 2, Q=3[/tex]
