A painter charges $25 per hour for interior work and $35 per hour for exterior work. If they spend 12 hours working and earn $350, what system of equations represents the situation?
a. $25x+35y=350, x+y=12$
b. $35x+25y=350, x+y=12$
c. $35x+25y-12, x+y=350$
d. $25x+35y=12, x+y=350
Answer (2)
Define variables: Let x be the hours for interior work and y be the hours for exterior work.
Write the earnings equation: 25 x + 35 y = 350 .
Write the total time equation: x + y = 12 .
The system of equations is: 25 x + 35 y = 350 and x + y = 12 , which corresponds to option a. 25 x + 35 y = 350 , x + y = 12 .
Explanation
Define Variables Let x be the number of hours the painter spends on interior work and y be the number of hours the painter spends on exterior work.
Write the Earnings Equation The painter charges $25 per hour for interior work and $35 per hour for exterior work. The total earnings are $350. This can be represented by the equation: 25 x + 35 y = 350
Write the Total Time Equation The painter spends a total of 12 hours working. This can be represented by the equation: x + y = 12
State the System of Equations Therefore, the system of equations that represents the situation is: 25 x + 35 y = 350
x + y = 12 This corresponds to option a.
Examples
Imagine a painter who needs to balance their workload between interior and exterior projects to meet a specific income goal. This problem helps the painter determine how many hours to allocate to each type of work. Understanding systems of equations can guide the painter in scenarios such as optimizing their work schedule, estimating project costs, or adjusting hourly rates to achieve desired earnings. This algebraic approach ensures efficient time management and financial planning in practical tasks.
The system of equations representing the situation is 25x + 35y = 350 and x + y = 12. This corresponds to option a from the choices provided. These equations capture the painter's earnings and total hours worked.
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