Question

Mrs. Blake needs to hire a babysitter. Kelsey charges $6 per hour plus a $5 fee. Lauren charges $4 per hour, plus a $10 fee. Mrs. Blake set up this equation to figure out for what amount of time both babysitters charge the same.
6h + 5 = 4h + 10
What is the correct sequence of steps to solve Mrs. Blake’s equation?

A. Subtract 6h from both sides. Subtract 5 from both sides. Divide each side by –2.
B. Subtract 4h from both sides. Subtract 5 from both sides. Divide each side by 2.
C. Subtract 4h from both sides. Add 5 to both sides. Divide each side by 2.
D. Subtract 4h from both sides. Subtract 5 from both sides. Divide each side by 6.

Answer 1

B) This way you'll get an answer of h=2.5

Answer 2

Answer:

Option B: Subtract 4h from both sides. Subtract 5 from both sides.Divide each side by 2.

Step-by-step explanation:

So why option B?

When solving equations one of the best method is to bring like terms together to a side (LHS or RHS) of the equation.

What are liked terms? This are numbers or integers with similar structure. From the question the liked terms are 5 and 10, and 6h and 4h.

Going by the workflow described in option B we will see that the end game here was to bring liked terms together.

So lets carry out the workflow step by step:

• Subtract 4h from both sides: 6h + 5 -4h = 4h + 10 -4h => 2h + 5 = 10
• Subtract 5 from both sides: 2h + 5 -5 = 10 -5 => 2h = 5 (Victory!!! we have succeeded in briinging like terms to a side)
• Divide each side by 2: 2h/2 = 5/2 => h = 2.5

So for the Babysitters to charge the same amount they have to have worked for 2.5 hours (that is 2 hours 30 minutes)