Question

1. $\frac{p}{4}+10 = 12$ is 8 the solution? 11. $-2y + 5 = -1$ is 3 the solution? 12. the fire department is having a bbq fundraiser. the hot dogs costs $1.50 each and cans of soda cost $0.75 each. the department uses the algebraic expression $1.50x + 0.75y$ to calculate customers total expenses. a. what does the $x$ variable represent? b. what does the $y$ variable represent? c. a family buys 7 hot dogs and 4 sodas. what are their total expenses?

Explanation:

Part a

Step1: Analyze the expression

The expression is \(1.50x + 0.75y\) and hot dogs cost \(\$1.50\) each. So the coefficient of \(x\) is the cost per hot dog.

Step2: Determine the meaning of \(x\)

Since the cost per hot dog is \(1.50\) and it's multiplied by \(x\), \(x\) should represent the number of hot dogs bought.

Step1: Analyze the expression

The expression is \(1.50x + 0.75y\) and sodas cost \(\$0.75\) each. So the coefficient of \(y\) is the cost per soda.

Step2: Determine the meaning of \(y\)

Since the cost per soda is \(0.75\) and it's multiplied by \(y\), \(y\) should represent the number of sodas bought.

Step1: Identify values for \(x\) and \(y\)

For hot dogs, \(x = 7\) (since 7 hot dogs are bought) and for sodas, \(y = 4\) (since 4 sodas are bought).

Step2: Substitute into the expression

Substitute \(x = 7\) and \(y = 4\) into \(1.50x+0.75y\).
First, calculate \(1.50\times7\): \(1.50\times7 = 10.5\)
Then, calculate \(0.75\times4\): \(0.75\times4=3\)

Step3: Sum the two results

Add the two amounts together: \(10.5 + 3=13.5\)

Answer:

The variable \(x\) represents the number of hot dogs.

Part b