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The 42 burgers are sold by Mrs. Garcia's class at $57.12 and 37 salad is sold by Mr. Runner’s class at $61.05.
What is a system of equation?
A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
Mrs. Garcia’s class sold burgers for $1.36 each and Mr. Runner’s class sold salads for $1.65 each. Together, the classes sold 79 items and earned $118.17 for their school.
- (a) Write a system of equations that model the problem.
Let x burgers are sold by Mrs. Garcia's class and s salad is sold by Mr. Runner’s class. Together, the classes sold 79 items for their school. Thus,
[tex]x + s = 79[/tex] .....1
Mrs. Garcia’s class sold burgers for $1.36 each and Mr. Runner’s class sold salads for $1.65 each. Together, the classes earned $118.17 for their school. Thus,
[tex]1.36(x) + 1.65(s) = 118.17\\1.36x + 1.65s = 118.17[/tex] ....2
- (b) Solve the systems of equations from part a.
Rewrite the first equation,
[tex]x + s = 79 \\ x = 79-s[/tex] .....3
Put this value of x in equation 2,
[tex]1.36(79-s) + 1.65s = 118.17\\107.44-1.36s + 1.65s = 118.17\\0.29s=118.17-107.44\\s=\dfrac{10.73}{0.29}\\s=37[/tex]
Put this value in equation 3,
[tex]x=79-37\\x=42[/tex]
- (c) Whose class sold more items?
42 burgers are sold by Mrs. Garcia's class and 37 salad is sold by Mr. Runner’s class. Thus, Mrs. Garcia's class sold more items.
- (d) Which class earned more money?
Money earned by Mrs. Garcia's class by selling 42 burger at $1.36 each is,
[tex]M_x=1.36\times42\\M_x=57.12[/tex]
Money earned by Mr. Runner’s class by selling 37 salad at $1.65 each is,
[tex]M_s=1.65\times37\\M_s=61.05[/tex]
Thus, Mr. Runner’s class earned more money.
Hence, the 42 burgers are sold by Mrs. Garcia's class at $57.12 and 37 salad is sold by Mr. Runner’s class at $61.05.
Learn more about the system of equations here;
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