Aced
05.05.2020 •
Mathematics
Tammy and Keith each work two part-time jobs in the summer mowing lawns and raking yards. Tammy
earns $10 for each lawn she mows and $5 for each yard she rakes. She wants to earn more than $200
from her part-time jobs. Keith earns $12 for each lawn he mows and $3 for each yard he rakes. He
wants to earn more than $180 from his part-time jobs.
A.) Write a system of linear inequalities to model the number of lawns they each mow (x) and the
number of yards they each rake (y).
Tammy:
Keith:
By the end of the summer, Tammy and Keith had mowed the same number of lawns and raked the same
number of yards. Keith had met his goal of earning more than $180 but Tammy did not meet her goal of
earning more than $200.
B.) What is a possible combination of the number of lawns they could have each mowed and the
number of yards they could have raked? Explain how you chose the combination and why you
know that combination is correct.
Solved
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Ответ:
A) Tammy: 10x + 5y > 200
Keith: 12x + 3y > 180
B) A possible combination is x = 16 and y = 4
Step-by-step explanation:
x: number of lawns they each mow
y: number of yards they each rake
A) Tammy earns $10 for each lawn she mows and $5 for each yard she rakes, then the total money she earns is computed by:
10x + 5y
She wants to earn more than $200, so her inequality is:
10x + 5y > 200
Keith earns $12 for each lawn he mows and $3 for each yard he rakes. He wants to earn more than $180. Then, his inequality is:
12x + 3y > 180
B) Keith had met his goal but Tammy did not meet her goal, then:
12x + 3y > 180
10x + 5y < 200
Let's suppose x = 16:
12(16) + 3y > 180
y > (180 - 192)/3
y > -4
10(16) + 5y < 200
y < (200 - 160)/5
y < 8
Then, a possible combination is x = 16 and y = 4
Ответ: