Define a variable and write an equation for each situation. Then solve.

Question

1. Bradley has a goal to work 28 hours each week at the pizza shop. So far he has worked 12 hours. How many more hours does he need to work to meet his goal?

2. Sheree is 4 times as old as Benjamin. If Sheree is 72 years old, how old is Benjamin?

Answer 1

Let's define the variables and write equations for each situation, then solve them.

Situation 1:

Define the variable: Let \( x \) be the number of hours Bradley still needs to work to meet his goal.

Write the equation: Bradley’s total goal of hours is 28, and he has already worked 12 hours. Therefore, the equation is: \[ x + 12 = 28 \]

Solve the equation: \[ x + 12 = 28 \] Subtract 12 from both sides: \[ x = 28 - 12 \] \[ x = 16 \]

Conclusion: Bradley needs to work 16 more hours to meet his goal.

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Situation 2:

Define the variable: Let \( b \) be Benjamin's age.

Write the equation: Sheree is 4 times as old as Benjamin, and Sheree is 72 years old. Therefore, the equation is: \[ 4b = 72 \]

Solve the equation: \[ 4b = 72 \] Divide both sides by 4: \[ b = \frac{72}{4} \] \[ b = 18 \]

Conclusion: Benjamin is 18 years old.