One summer a football camp orders $40$ footballs from a website. Including the one-time shipping fee, the total cost is $\$ 685$ . The next year the camp orders $70$ footballs for the same website and pays $\$ 1135$ including the same shipping fee. $\newline$ What is the cost per football? $\newline$ Submit $\newline$ What is the one-time shipping fee? $\newline$ Submit

Full solution

Q. One summer a football camp orders

40

footballs from a website. Including the one-time shipping fee, the total cost is

\$ 685

. The next year the camp orders

70

footballs for the same website and pays

\$ 1135

including the same shipping fee.

\newline

What is the cost per football?

\newline

Submit

\newline

What is the one-time shipping fee?

\newline

Submit

Define Variables: Let's call the cost per football ＂ $x$ ＂ and the one-time shipping fee ＂ $y$ ＂. So the total cost for the first year is $40x + y = \$(685)$ .
First Year Total Cost: For the second year, the total cost is $70x + y = \$(1135)$ .
Elimination Method: Now we got two equations, let's solve them using the elimination method. Subtract the first equation from the second to eliminate $y$ .
Simplify Equation: So, $(70x + y) - (40x + y) = (\$1135) - (\$685)$ . This simplifies to $30x = (\$450)$ .
Calculate Cost per Football: Divide both sides by $30$ to find the cost per football. $x = \frac{\$(450)}{30}$ .
Find Shipping Fee: $x = \$($15$) \text{ per football}.
Plug in Values: Now, plug the value of $x$ back into one of the equations to find $y$. Let's use the first year's equation: $40(15) + y = \$(685)$.
Calculate Total: Calculate $40 \times 15$, which is $\$600$. So, $\$600 + y = \$685$.
Subtract to Find Shipping Fee: Subtract $\$600$ from both sides to find $y$. $y = \$685 - \$600$.
Subtract to Find Shipping Fee: Subtract $\$600$ from both sides to find $y$. $y = \$685 - \$600.$ $y = \$85.$ So the one-time shipping fee is $\$85.$