Question

Ellie has a 10-pound bag of sugar to make some treats. To make cookies, she needs 0.5 pounds of sugar, and to make fudge, she needs 2.25 pounds of sugar. She wants to use twice as much sugar for the cookies as for the fudge. If c = the number of batches of cookies and f = the number of batches of fudge, choose the system of equations that models this situation.

a 0.5c + 2.25f = 10
b 0.5c + 2.25f = 10
c.5c + 2.25f = 10
d.5c + 2.25f = 10

Answer 1

The correct system of equations to model Ellie's situation is 0.5c = 4.5f and 0.5c + 2.25f = 10. This system reflects the requirement of using twice as much sugar for cookies as for fudge, and the total sugar used not exceeding the 10-pound bag she has.

Step-by-step explanation:

Ellie has a 10-pound bag of sugar and wants to use twice as much sugar for cookies as for fudge. If c represents the number of batches of cookies and f represents the number of batches of fudge, we can establish the following relationships:

• Each batch of cookies requires 0.5 pounds of sugar, so the total sugar for cookies is 0.5c.
• Each batch of fudge requires 2.25 pounds of sugar, so the total sugar for fudge is 2.25f.
• Ellie wants to use twice as much sugar for cookies as for fudge, which gives us the equation 2(2.25f) = 0.5c or 4.5f = 0.5c.
• All the sugar used must add up to 10 pounds, which gives us the second equation 0.5c + 2.25f = 10.

Combining the two equations, we can form a system of equations that models the situation:

1. 0.5c = 4.5f
2. 0.5c + 2.25f = 10