Kimberly and Autumn visited a candy store at a theme park. Kimberly spent a total of $22 and bought 3 lollipops and 5 gumballs. Autumn bought 4 lollipops and 5 gumballs and paid $26.

Question

Which system of equations can be used to determine the price per lollipop, I, and the price of gumballs, g?
a.31 + 4g = 22 51 + 5g = 26
b.31 + 5g = 22 41 + 5g = 26
c.51 + 3g = 22 51 + 4g = 26
d.31 + 5g = 26 41 + 5g = 22

Answer 1

To find the system of equations that can be used to determine the price per lollipop (I) and the price of gumballs (g), we can set up the following equations based on the information given:

1. Kimberly's purchase can be expressed as: \[ 3I + 5g = 22 \] This equation comes from Kimberly buying 3 lollipops and 5 gumballs totaling $22.

2. Autumn's purchase can be expressed as: \[ 4I + 5g = 26 \] This equation comes from Autumn buying 4 lollipops and 5 gumballs totaling $26.

Now we can check which option matches the equations we derived:

• a. \(3I + 4g = 22\) and \(5I + g = 26\)
• b. \(3I + 5g = 22\) and \(4I + 5g = 26\)
• c. \(5I + 3g = 22\) and \(5I + 4g = 26\)
• d. \(3I + 5g = 26\) and \(4I + 5g = 22\)

The correct system of equations corresponding to our derived equations is:

b. \(3I + 5g = 22\) and \(4I + 5g = 26\)

So the answer is b.