Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y). She has 30 coins altogether.
A) x = 30 - y, 0.10x + 0.25y = 3.50
B) $x - y = 30,0.10 x + 0.25 y = 3.50$
C) y - x = 30, 0.10x + 0.25y = 3.50
D) x + y = 30, 0.05x + 0.25y = 3.50
E) $x + y = 30,0.05 y + 0.25 x = 3.50$

Question

Quizplus · Accepted Answer

We can use the system of equations: 
x + y = 30 (since there are 30 coins altogether) 
0.10x + 0.25y = 3.50 (since Nancy has only dimes and quarters and has $3.50 in total) 
Simplifying the first equation, we get x = 30 - y. This can be substituted into the second equation to get 0.10(30-y) + 0.25y = 3.50, which is the same as 3 - 0.15y = 3.50. Solving for y, we get y = 10. Substituting this back into the first equation, we get x = 20. Therefore, Nancy has 20 dimes and 10 quarters. Choice A correctly represents this system of equations.

Write a System of Equations to Describe the Problem Situation x−y=30,0.10x+0.25y=3.50x - y = 30,0.10 x + 0.25 y = 3.50x−y=30,0.10x+0.25y=3.50

Write a System of Equations to Describe the Problem Situation $x - y = 30,0.10 x + 0.25 y = 3.50$