Beth and Ben work together in a store. The expression $12h+50$ represents the amount of money Beth earns, and the expression $14h-20$ represents the amount of money that Ben earns. The variable $h$ represents hours worked, and the integers represent dollar amounts. Find an expression that gives the total amount of money earned by Beth and Ben when they work together for $h$ hours.
A. $26h+70$
B. $26h+30$
C. $2h+70$
D. $2h+30
Answer (2)
Add Beth's earnings ( 12 h + 50 ) and Ben's earnings ( 14 h − 20 ).
Combine the 'h' terms: 12 h + 14 h = 26 h .
Combine the constant terms: 50 − 20 = 30 .
The total earnings expression is 26 h + 30 .
Explanation
Understanding the Problem We are given two expressions, one representing Beth's earnings and the other representing Ben's earnings. We need to find the total earnings when they work together.
Setting up the Addition Beth's earnings: 12 h + 50 Ben's earnings: 14 h − 20 To find the total earnings, we add the two expressions:
Adding the Expressions ( 12 h + 50 ) + ( 14 h − 20 )
Combining Like Terms Now, we combine like terms. We add the terms with 'h' and the constant terms separately: ( 12 h + 14 h ) + ( 50 − 20 )
Simplifying the Expression 26 h + 30
Final Answer So, the expression that represents the total amount of money earned by Beth and Ben when they work together for h hours is 26 h + 30 .
Examples
Imagine Beth and Ben are selling lemonade. Beth earns $12 for every hour she works plus a fixed $50 from previous sales. Ben earns $14 per hour but had to spend $20 initially on supplies. The expression 26 h + 30 tells us their combined earnings for any number of hours they work together. For example, if they work for 5 hours, their total earnings would be $26(5) + 30 = $130 + 30 = $160. This kind of calculation helps them understand their combined profitability and plan their work schedule effectively.
The total amount of money earned by Beth and Ben when they work together for h hours is represented by the expression 26 h + 30 . Therefore, the correct answer is option B: 26 h + 30 .
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