Q71. - Algebra 1

Question

Student Council has a budget of \(1000 for the homecoming dance. So far, they have spent \)350 dollars for music?

1. Write an equation to represent the amount of money left to spent. Then solve the equation.
2. They then spent \(225 on decorations. Write an equation to represent the amount of money left.
3. If the student Council spent their entire budget, write an equation to represent how many \)6 tickets they must sell to make a profit.

Step-by-Step Solution

Answer

1. The money left to spent $=\$700$
2. The money left to spent $=475$
3. Number of tickets $=167$

Part a. Step 1. Given information.

Total money $=\$1000$.

Money spent on music $=\$350$.

Part a. Step 2. Introduce the variable.

Consider the money left be x.

Part a. Step 3. Write the equation.

Since, the total money is $1000.

Therefore,

$x+300=1000$

Part a. Step 4. Solve the equation.

Take the equation $x+300=1000$.

 

Subtract 300 from both sides of above equation.

$$\begin{gathered} x+300-300=1000-300 \\ x=1000-300 \end{gathered}$$

So,

$x=\$700$

Part b. Step 1. Given information.

Total money $=\$1000$.

Money spent on music $=\$225$.

Money spent on decorations $=\$350$.

Part b. Step 2. Introduce the variable.

Consider the money left be x.

Part b. Step 3. Write the equation.

Since, students spent $300 for music and then $225 on decorations.

 

Therefore,

$$\begin{gathered} x+300+225=1000 \\ x+525=1000 \end{gathered}$$

Part b. Step 4. Solve the equation.

Take the equation $x+525=1000$.

 

Subtract 525 from both sides of the above equation.

 $$\begin{gathered} x+525-525=1000-525 \\ x=1000-525 \end{gathered}$$

So,

width="64" style="max-width: none; vertical-align: -4px;" $x=\$475$

Part c. Step 1. Given information.

Total money $=\$1000$.

Part c. Step 2. Introduce the variable.

Consider the number of tickets be x.

Part c. Step 3. Write the equation.

Since, total price of tickets $=\$6$

 

Therefore,

$6x>1000$

Part c. Step 4. Solve the equation.

Take the equation $6x>1000$. This can be written as:

 

$$\begin{gathered} x>\frac{1000}{6} \\ x>166.66 \end{gathered}$$

 

So,

$x=167 \text{tickets}$