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The cost of 4 hammers and 6 wrenches was $68. The cost of 5 hammers and 8 wrenches was $87. What are the prices of a hammer and a wrench?

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:

  1. For 4 hammers and 6 wrenches costing $68:
    [tex]4H + 6W = 68[/tex]

  2. 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:

  1. [tex]2H + 3W = 34[/tex]
  2. [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:

  1. [tex]10H + 15W = 170[/tex]
  2. [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

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