Question

Lisa is in charge of buying door prizes for the school dance. She bought 100 items made up of $2 cups and $3 bracelets that commemorate the dance. The total cost for the items was $260. Without knowing the numbers of each item Lisa bought, Sandra writes this system of equations to figure it out on her own.

c + b = 100
2c + 3b = 260

Answer 1

To solve this system of equations, we can use the method of substitution. Lisa bought 40 cups and 60 bracelets.

Step-by-step explanation:

To solve this system of equations, we can use the method of substitution. We have two equations:

c + b = 100

2c + 3b = 260

We can solve the first equation for c:

c = 100 - b

Now we can substitute this value of c into the second equation:

2(100 - b) + 3b = 260

Expanding the equation:

200 - 2b + 3b = 260

Combining like terms:

b + 200 = 260

Subtracting 200 from both sides:

b = 60

Now we can substitute this value of b back into the first equation to find c:

c + 60 = 100

Subtracting 60 from both sides:

c = 40

Therefore, Lisa bought 40 cups and 60 bracelets.