Question

Calvin and Sara went to the candy store. Calvin bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60.Use the system of equations to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

Answer 1

We are given that Calvin bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. If the cost of each fudge is "f" and the cost of each gum is "g", then the equation representing the purchase for Calvin is:

`5f+3g=5.7,(1)`

This is our first equation.

We are also given that Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. The equation representing the purchase for Sara is

`2f+10g=3.6,(2)`

This is our second equation.

To solve the system we will solve for "f" in equation (1). To do that we will subtract "3g" from both sides:

`\begin{gathered} 5f+3g-3g=5.7-3g \\ 5f=5.7-3g \end{gathered}`

Now we divide both sides by 5:

`f=(5.7-3g)/(5)`

Now we substitute this value in equation (1):

`2((5.7-3g)/(5))+10g=3.6`

Now we divide the equation by 2, we get:

`(5.7-3g)/(5)+(10g)/(2)=(3.6)/(2)`

Simplifying we get:

`(5.7-3g)/(5)+5g=1.8`

Now we multiply both sides by 5:

`5.7-3g+25g=9`

Now we add like terms:

`5.7+22g=9`

Now we subtract 5.7 to both sides, we get:

`\begin{gathered} 5.7-5.7+22g=9-5.7 \\ 22g=3.3 \end{gathered}`

Now we divide both sides by 22:

`\begin{gathered} (22g)/(22)=(3.3)/(22) \\ \\ g=0.15 \end{gathered}`

Now, we substitute this value in equation (1) where we have already solved for "f":

`f=(5.7-3g)/(5)`

Substituting the value of "g" we get:

`f=(5.7-3(0.15))/(5)`

Now we solve the operations, we solve the product:

`f=(5.7-0.45)/(5)`

Now we solve the operations:

`f=(5.25)/(5)=1.05`

Therefore, the price of gums is $0.15 and the price of fudge is $1.05.