a What happens to the budget for the homecoming dance when the Student Council spends $350?
B
b How does the amount from Part A change if they spend $250 more?
C
c How much must they earn on the tickets to make a profit?
A
aExample Equation:m=1000−350
Solution:m=$650
B
bExample Equation:m=1000−350−225
Solution:m=$425
C
cExample Equation:6t=1000
Solution:167
Practice makes perfect
a Let m be the amount of money the Student Council has left to spend. We know that they have spent $350 for music, and that their budget for the homecoming dance was $1000.
mis$1000minus$350
Let's write it as an equation! The first part m is ... tells us that m is equal to something.
m=…
What do we put on the right-hand side of the equation? Well, we can rewrite minus as −, so we can write our equation as follows.
m=1000−350
To solve the equation we have to evaluate the expression on the right-hand side.
The solution is m=650, which tells us that the Student Council has $650 left to spend.
b From Part A, we already know the equation for the amount of money left.
m=1000−350
We also now know that the Student Council spent $225 on decorations. Therefore, we have to subtract an additional 225 from 1000−350 dollars, as this is the amount which was left before. This gives us a new equation for the amount left.
m=1000−350−225
Let's evaluate the expression on the right-hand side to solve it!
The solution is m=425, which tells us that now the Student Council has $425 left to spend.
c Let t be the number of tickets the Student Council must sell to make a profit. Since each ticket is $6, their earnings can be described by the following expression.
6⋅t⇔6t
The budget for the homecoming dance was $1000. If the Student Council wants to make a profit after spending the entire budget, they must earn at least this much selling the tickets. Therefore, we get the following equation.
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