the local skating rink pays mary a fixed rate per pupil plus a base amount to work as a skating instructor…

the local skating rink pays mary a fixed rate per pupil plus a base amount to work as a skating instructor. she earns $90 for instructing 15 students on monday afternoon. last friday, she earned $62 for working with 8 students. lisa is also a skating instructor. she receives half the base amount that mary does, but she is paid twice as much per student. who would earn more money instructing a class of 20 students?- lisa would earn $120 more than mary.- lisa would earn $65 more than mary.- mary would earn $15 more than lisa.- mary would earn $10 more than lisa.

the local skating rink pays mary a fixed rate per pupil plus a base amount to work as a skating instructor. she earns $90 for instructing 15 students on monday afternoon. last friday, she earned $62 for working with 8 students. lisa is also a skating instructor. she receives half the base amount that mary does, but she is paid twice as much per student. who would earn more money instructing a class of 20 students?- lisa would earn $120 more than mary.- lisa would earn $65 more than mary.- mary would earn $15 more than lisa.- mary would earn $10 more than lisa.

Answer

Explanation:

Step1: Define variables for Mary

Let $b$ = Mary's base amount, $r$ = rate per pupil for Mary.

Step2: Set up equations for Mary

From Monday: $b + 15r = 90$ From Friday: $b + 8r = 62$

Step3: Solve for $r$

Subtract Friday's equation from Monday's: $$(b + 15r) - (b + 8r) = 90 - 62$$ $$7r = 28$$ $$r = \frac{28}{7} = 4$$

Step4: Solve for Mary's base $b$

Substitute $r=4$ into $b + 8r = 62$: $$b + 8(4) = 62$$ $$b + 32 = 62$$ $$b = 62 - 32 = 30$$

Step5: Find Lisa's pay parameters

Lisa's base = $\frac{b}{2} = \frac{30}{2} = 15$ Lisa's rate per pupil = $2r = 2(4) = 8$

Step6: Calculate Mary's pay for 20 students

$$b + 20r = 30 + 20(4) = 30 + 80 = 110$$

Step7: Calculate Lisa's pay for 20 students

$$15 + 20(8) = 15 + 160 = 175$$

Step8: Find the difference

$$175 - 110 = 65$$

Answer:

Lisa would earn $65 more than Mary.