Could I get some help Please
The cost of 4 baseball bats and 3 softball bats is $389. If the baseball bats cost $10 less than the twice the hat, write an equation to model the situation so that we can find the cost of the hat and the baseball bat.
Don’s plumbing charges a fee of $75 for an inspection plus $25 per hour for labor. Paul’s plumbing charges $45 per hour for labor. Write an inequality to model the situation so that we can find how many hours of labor is required so that the total cost for hiring Don’s Plumbing is less total cost of hiring Paul’s plumbing?
you still on
Yes
If the softball bat costs $x, then
4(2x-10) + 3x = 389
75 + 25x < 45x
thx oobleck what about the second one
geez, did you not read everything I posted? and note the relation between the two equations and the two questions?
Sure, I can help you with both questions.
Question 1: Let's define the variables:
Let B represent the cost of a baseball bat.
Let S represent the cost of a softball bat.
According to the problem:
The cost of 4 baseball bats is 4B.
The cost of 3 softball bats is 3S.
The total cost of 4 baseball bats and 3 softball bats is $389.
We are also given that:
The baseball bats cost $10 less than twice the cost of a hat.
Using this information, we can write the equation:
4B + 3S = 389
Now, we need to express the relationship stated in the second condition:
The baseball bats cost $10 less than twice the cost of a hat.
Therefore, we can write another equation:
B = 2S - 10
By solving these two equations simultaneously, we can find the values of B and S, which represent the cost of a baseball bat and a softball bat, respectively.
Question 2: Let's define the variables:
Let D represent the total cost for hiring Don's Plumbing.
Let P represent the total cost for hiring Paul's Plumbing.
Let H represent the number of labor hours required.
According to the problem:
Don’s plumbing charges $75 for an inspection plus $25 per hour for labor. So the total cost for Don's Plumbing can be expressed as:
D = 75 + 25H
Paul’s plumbing charges $45 per hour for labor. So the total cost for Paul's Plumbing can be expressed as:
P = 45H
Now, the requirement is to find how many hours of labor (represented by H) is required so that the total cost for hiring Don’s Plumbing is less than the total cost of hiring Paul’s Plumbing.
In mathematical terms, this can be represented as the following inequality:
D < P
Substituting the expressions for D and P, we get:
75 + 25H < 45H
Simplifying the inequality, we have:
75 < 20H
Dividing both sides by 20, we get:
3.75 < H
Therefore, the number of labor hours required, H, should be greater than 3.75 (or 4, if we consider whole numbers) in order for the total cost for hiring Don’s Plumbing to be less than the total cost of hiring Paul’s Plumbing.