Question

1. a secondary school has a $1000 budget for its phys - ed department. soccer balls cost $25 each, basketballs cost $30 each, and jerseys are $20 each.

a) write an algebraic equation that can be used to represent the schools budget.
b = 1000+25s + 30b+20j
b) assume the school purchases 8 basketballs, 8 soccer balls, and 15 jerseys. input the numbers into your algebraic equation to determine how much money is remaining in the budget.

Explanation:

Step1: Define variables and write equation

Let $s$ be the number of soccer - balls, $b$ be the number of basketballs, and $j$ be the number of jerseys. The total cost of purchases plus the remaining budget $R$ equals the initial budget. The initial budget is $1000$. So the equation is $25s + 30b+20j+R = 1000$, or $R=1000 - 25s - 30b - 20j$.

Step2: Substitute values

We are given that $s = 8$, $b = 8$, and $j = 15$. Substitute these values into the equation for $R$:
$R=1000-25\times8 - 30\times8-20\times15$.
First, calculate each product:
$25\times8 = 200$, $30\times8 = 240$, and $20\times15 = 300$.
Then, $R=1000-(200 + 240+300)$.
$R=1000 - 740$.
$R = 260$.

Answer:

a) $1000=25s + 30b+20j+R$ (or $R = 1000 - 25s - 30b - 20j$)
b) $260$