Answer:
GIVEN THAT:
Number of screws costing $0.25 as x
Number of bolts costing $0.40 as y
From the given information:
The total cost of the mixture is $3.10
The number of $0.25 pieces is 2 more than the number of $0.40 pieces
The cost equation is: $0.25x + $0.40y = $3.10
The quantity equation is: x = y + 2
By substituting x = y + 2 into the cost equation:
$0.25(y + 2) + $0.40y = $3.10
Simplifying: $0.25y + $0.50 + $0.40y = $3.10
Combining like terms: $0.65y + $0.50 = $3.10
Solving for y: $0.65y = $2.60
y = 4 (number of bolts)
Substitute y = 4 back into x = y + 2:
x = 4 + 2
x = 6 (number of screws)
Therefore, Mr. Harvey should include 6 screws and 4 bolts in the package.
hope it's helpful
Answer:
6 screws
4 bolts
Step-by-step explanation:
To solve this problem, we can set up a system of equations based on the given information.
Let s be the number of screws costing $0.25 each.
Let b be the number of bolts costing $0.40 each.
Given that a mixture of screws and bolts costs $3.10, this can be expressed as :
[tex]0.25s + 0.40b = 3.10[/tex]
Given that the number of screws is 2 more than the number of bolts, then:
[tex]s = b + 2[/tex]
Therefore, the system of equations is:
[tex]\begin{cases}0.25s + 0.40b = 3.10\\s = b + 2\end{cases}[/tex]
To solve this system of equations, substitute the second equation into the first equation and solve for b:
[tex]0.25(b + 2) + 0.40b = 3.10\\\\0.25b + 0.50 + 0.40b = 3.10\\\\0.65b + 0.50 = 3.10\\\\0.65b = 3.10 - 0.50\\\\0.65b = 2.60\\\\b = 2.60 \dov 0.65\\\\b=4[/tex]
Therefore, 4 bolts are included in the package.
To find the number of screws, substitute b = 4 into the second equation:
[tex]s = 4 + 2\\\\s = 6[/tex]
Therefore, 6 screws are included in the package.