Respuesta :
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:
[tex]5f+3g=5.7,(1)[/tex]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
[tex]2f+10g=3.6,(2)[/tex]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:
[tex]\begin{gathered} 5f+3g-3g=5.7-3g \\ 5f=5.7-3g \end{gathered}[/tex]Now we divide both sides by 5:
[tex]f=\frac{5.7-3g}{5}[/tex]Now we substitute this value in equation (1):
[tex]2(\frac{5.7-3g}{5})+10g=3.6[/tex]Now we divide the equation by 2, we get:
[tex]\frac{5.7-3g}{5}+\frac{10g}{2}=\frac{3.6}{2}[/tex]Simplifying we get:
[tex]\frac{5.7-3g}{5}+5g=1.8[/tex]Now we multiply both sides by 5:
[tex]5.7-3g+25g=9[/tex]Now we add like terms:
[tex]5.7+22g=9[/tex]Now we subtract 5.7 to both sides, we get:
[tex]\begin{gathered} 5.7-5.7+22g=9-5.7 \\ 22g=3.3 \end{gathered}[/tex]Now we divide both sides by 22:
[tex]\begin{gathered} \frac{22g}{22}=\frac{3.3}{22} \\ \\ g=0.15 \end{gathered}[/tex]Now, we substitute this value in equation (1) where we have already solved for "f":
[tex]f=\frac{5.7-3g}{5}[/tex]Substituting the value of "g" we get:
[tex]f=\frac{5.7-3(0.15)}{5}[/tex]Now we solve the operations, we solve the product:
[tex]f=\frac{5.7-0.45}{5}[/tex]Now we solve the operations:
[tex]f=\frac{5.25}{5}=1.05[/tex]Therefore, the price of gums is $0.15 and the price of fudge is $1.05.
