Select the correct answer.

During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410. If $x$ represents the number hours she babysat and $y$ represents the number of hours she did yardwork, which system of equations models this situation?

A. $\begin{array}{l}x+y=34 \ 10 x+15 y=410\end{array}$
B. $x+y=410$
$10 x+15 y=34$
C. $x+y=34$
$15 x+10 y=410$
D. $x+y=410$
$15 x+10 y=34$

Question

Select the correct answer. 
 
During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410. If $x$ represents the number hours she babysat and $y$ represents the number of hours she did yardwork, which system of equations models this situation? 
 
A. $\begin{array}{l}x+y=34 \ 10 x+15 y=410\end{array}$ 
B. $x+y=410$ 
$10 x+15 y=34$ 
C. $x+y=34$ 
$15 x+10 y=410$ 
D. $x+y=410$ 
$15 x+10 y=34$

GinnyAnswer · Answer

Define x as hours babysitting and y as hours doing yardwork. 
 Write the equation for total hours: x + y = 34 . 
 Write the equation for total earnings: 10 x + 15 y = 410 . 
 The system of equations is { x + y = 34 10 x + 15 y = 410 ​ , which corresponds to option A. A ​ 
 
 Explanation 
 
 Define variables and write first equation Let x be the number of hours Jody spent babysitting and y be the number of hours she spent doing yardwork. We know that the total number of hours she worked is 34, so we can write the equation: 
 
 First equation x + y = 34 
 
 Write second equation based on earnings We also know that Jody earns $10 per hour babysitting and $15 per hour doing yardwork, and that she earned a total of $410 this week. So, we can write the equation: 
 
 Second equation 10 x + 15 y = 410 
 
 System of equations Now, we have a system of two equations with two variables: 
 
 The system { x + y = 34 10 x + 15 y = 410 ​ 
 
 Compare with options Comparing this system of equations with the given options, we see that it matches option A. 
 
 Final Answer Therefore, the correct answer is A.

Examples 
 Systems of equations are useful in many real-world situations. For example, suppose you are planning a party and need to buy snacks. You know that chips cost $3 per bag and soda costs $2 per bottle. You have a budget of $30 and want to buy a total of 12 items. You can set up a system of equations to determine how many bags of chips and bottles of soda you can buy. Let c be the number of bags of chips and s be the number of bottles of soda. The equations would be c + s = 12 and 3 c + 2 s = 30 . Solving this system will tell you how many of each item you can purchase within your budget and quantity constraints.

Answer (1)

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