A high school basketball team has a budget specifically for towels and extra basketballs. A towel costs $4 and a basketball costs $22. Assume the budget is $350 and that 30 towels are needed for the team for the entire season. Use a standard form equation to determine how many basketballs may be purchased by the team.
10
To determine how many basketballs the team can purchase within their budget, we need to set up a standard form equation.
Let's assign variables to the unknown quantities:
Let x be the number of basketballs the team can purchase.
The cost of 30 towels is $4 each, so the total cost of the towels can be calculated as:
Total cost of towels = 30 towels × $4/towel = $4 × 30 = $120
The cost of x basketballs is $22 each, so the total cost of the basketballs can be calculated as:
Total cost of basketballs = x basketballs × $22/basketball = $22x
The total budget for towels and basketballs is given as $350.
So, the standard form equation can be set up as:
Total cost of towels + Total cost of basketballs = Total budget
$120 + $22x = $350
Simplifying the equation, we have:
$22x + $120 = $350
Now, we can solve for x (the number of basketballs) by rearranging the equation and isolating x:
$22x = $350 - $120
$22x = $230
Dividing both sides by $22, we get:
x = $230 / $22
Using a calculator, we find that x is approximately 10.45.
Since basketballs cannot be purchased in fractional quantities, the team can purchase a maximum of 10 basketballs within their budget.