Question

Solve the following word problem by using a system of equations.

Jake and his friends went to the carnival. The total number of ice cream sandwiches and sodas purchased among all of them was 18. One ice cream sandwich costs $2.25 and a soda costs 75¢. In total, $30.00 was spent on ice cream and soda.

Which statement is true?

A.
Jake went to the carnival with 8 of his friends.

B.
Jake and his friends bought a total of 11 ice cream sandwiches.

C.
Jake and his friends bought a total of 11 sodas.

D.
Jake and his friends spent more on sodas than ice cream sandwiches.

Answer 1

For this problem, we can use systems of equations. I will use the variables x  (for ice-cream) and y (for soda). We get the system:

2.25x+0.75y=30.00
x+y=18

Putting the second equation in terms of y, we get that y=-x+18. We can substitute this into our first equation.

2.25x+0.75y=30.00
becomes
2.25x+0.75(-x+18)=30

Solving for x, we get that x=11. This satisfies answer B.

However, if you want to check to see if this is correct, you could find y by plugging in your value of x into the first equation, then check to see if your found values satisfy BOTH equations.

2.25(11)+0.75y=30
24.75+0.75y=30
0.75y=5.25
y=7

Then we plug this into both equations to see if they are true.

2.25(11)+0.75(7)=30
24.75+5.25=30
30=30 (This is true)

x+y=18
11+7=18
18=18 (This is true).

Both equations are true, so the value for x and y are correct. We see that only answer B is supported through analyzing your work.

:)