Linda works at a pharmacy for $15 an hour. She also babysits for $10 an hour. Linda needs to earn at least $90 per week, but she does not want to work more than 20 hours per week. Show and describe the number of hours Linda could work at each job to meet her goals. List two possible solutions.
Let our two variables be:
p # of pharmacy hours
b # of babysitting hours
Then we should have two statements from the given facts:
and
We can graph these inequalities by solving for either p or b in both inequality.
Once the inequalities are graphed then any point that is shaded in their intersection will work.
Let me know if that helped you please (:
p+b less than or equal to 20 and 15*p+10*b is greater than or equal to 90
Tony wants to plant at least 40 acres of corn and at least 50 acres of soybeans. He wants no more than 200 acres of corn and soybeans. Show and describe all the possible combination's of the number of acres of corn and of soybeans Tony could plant. List two possible combination's
To find out the number of hours Linda could work at each job, we can set up an inequality based on the given information.
Let's use the variables:
- x: the number of hours Linda works at the pharmacy
- y: the number of hours Linda babysits
We are given the following conditions:
1. Linda earns $15 an hour at the pharmacy, so the amount she earns from the pharmacy job can be calculated as 15x.
2. Linda earns $10 an hour from babysitting, so the amount she earns from babysitting can be calculated as 10y.
3. Linda needs to earn at least $90 per week. Therefore, the total amount Linda earns must be at least $90, which can be represented as the inequality: 15x + 10y ≥ 90.
4. Linda does not want to work more than 20 hours per week. This gives us the condition: x + y ≤ 20.
Based on these conditions, let's find two possible solutions:
Solution 1:
Let's assume Linda works 0 hours at the pharmacy (x = 0) and works 9 hours babysitting (y = 9). In this case:
- Linda earns 0 dollars from the pharmacy (15x = 15 * 0 = $0).
- Linda earns $90 from babysitting (10y = 10 * 9 = $90).
- The total amount she earns is $0 + $90 = $90, which meets her goal.
- The total number of hours worked is 0 + 9 = 9 hours.
Solution 2:
Let's assume Linda works 5 hours at the pharmacy (x = 5) and works 10 hours babysitting (y = 10). In this case:
- Linda earns $75 from the pharmacy (15x = 15 * 5 = $75).
- Linda earns $100 from babysitting (10y = 10 * 10 = $100).
- The total amount she earns is $75 + $100 = $175, which exceeds her goal of $90.
- The total number of hours worked is 5 + 10 = 15 hours.
So, two possible solutions for Linda to meet her goals are:
1. Working 0 hours at the pharmacy and 9 hours babysitting, for a total of 9 hours worked.
2. Working 5 hours at the pharmacy and 10 hours babysitting, for a total of 15 hours worked.