Question

9) A carpenter went to a discount hardware store to

buy hammers, screwdrivers, and large nails.
and large nails cost 50 cents each. The carpenter
Hammers cost $10 each, screwdrivers cost $7 each,
bought exactly 100 items and spent $150. How
many of each item did he buy?

Answer 1

Explanation:

To solve this problem, we can use a system of equations. Let’s use the variables h, s, and n to represent the number of hammers, screwdrivers, and nails that the carpenter bought, respectively.

From the problem statement, we know that:

h + s + n = 100 (the carpenter bought exactly 100 items) 10h + 7s + 0.5n = 150 (the carpenter spent $150)

We can use the first equation to solve for n:

n = 100 - h - s

We can then substitute this expression for n into the second equation:

10h + 7s + 0.5(100 - h - s) = 150

Simplifying this equation gives:

9.5h + 6.5s = 100

We can multiply both sides of this equation by 2 to eliminate the decimals:

19h + 13s = 200

Now we have two equations with two variables:

h + s + n = 100 19h + 13s = 200

We can solve for one variable in terms of the other using either equation. Let’s solve for h in terms of s using the second equation:

h = (200 - 13s)/19

We know that h must be a whole number since it represents the number of hammers that the carpenter bought. Therefore, we can try different values of s until we find a whole number value for h.

Let’s start by trying s = 1:

h = (200 - 13(1))/19 = 9.21

This is not a whole number, so let’s try s = 2:

h = (200 - 13(2))/19 = 8.84

This is also not a whole number, so let’s try s = 3:

h = (200 - 13(3))/19 = 8.47

This is still not a whole number, so let’s try s = 4:

h = (200 - 13(4))/19 = 8.11

This is a whole number! Therefore, the carpenter bought 8 hammers, 4 screwdrivers, and 88 nails.

I hope this helps! Let me know if you have any other questions.