Respuesta :
we can translate the given statements into algebraic expressions. In this case,
0.05x + 0.10y + 0.25z = 4.65z = 3 + yx = 2 z
solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11
For this case we have the following variables:
x: number of nickels
y: number of dimes
z: number of quarters
We now write the system of equations that models the problem:
[tex] 0.05x + 0.1y + 0.25z = 4.65 z = y + 3 x = 2z [/tex]
Rewriting the equations as a function of z we have:
[tex] 0.05 (2z) + 0.1 (z-3) + 0.25z = 4.65 [/tex]
From here, we clear the value of z:
[tex] 0.1z + 0.1z - 0.3 + 0.25z = 4.65 0.1z + 0.1z + 0.25z = 4.65 + 0.3 0.1z + 0.1z + 0.25z = 4.65 + 0.3 0.45z = 4.95 [/tex]
[tex] z = \frac{4.95}{0.45} z = 11 [/tex]
Answer:
The number of quarters that Rachna has is:
B. 11