Answer :
The cost of one hammer is $11 and the cost of one wrench is $4.
To find the prices of the hammers and wrenches, we can set up a system of equations based on the information provided.
Let:
- H = the price of one hammer
- W = the price of one wrench
From the problem, we have the following two equations based on the cost of hammers and wrenches:
For 4 hammers and 6 wrenches costing $68:
[tex]4H + 6W = 68[/tex]For 5 hammers and 8 wrenches costing $87:
[tex]5H + 8W = 87[/tex]
Now we can solve this system of equations step-by-step.
Step 1: Simplify the Equations
We can simplify Equation 1 by dividing all terms by 2:
[tex]2H + 3W = 34[/tex]
Now, our equations are:
- [tex]2H + 3W = 34[/tex]
- [tex]5H + 8W = 87[/tex]
Step 2: Use Substitution or Elimination
We can use the elimination method to eliminate one variable. Let's multiply the first equation by 5:
[tex]10H + 15W = 170[/tex] (This will be our new Equation 3)
Now, we have:
- [tex]10H + 15W = 170[/tex]
- [tex]5H + 8W = 87[/tex]
Next, multiply the second equation by 2:
[tex]10H + 16W = 174[/tex] (This will be our new Equation 4)
Now subtract Equation 3 from Equation 4:
[tex](10H + 16W) - (10H + 15W) = 174 - 170[/tex]
[tex]W = 4[/tex]
Step 3: Substitute W back into one of the equations
Now that we have [tex]W = 4[/tex], we can substitute it back into the first simplified equation:
[tex]2H + 3(4) = 34[/tex]
[tex]2H + 12 = 34[/tex]
[tex]2H = 34 - 12[/tex]
[tex]2H = 22[/tex]
[tex]H = 11[/tex]
Final prices:
- Price of one hammer (H) = $11
- Price of one wrench (W) = $4