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James bought 24 bolts at the hardware store for a total of $9.00. Some were 3-inch bolts that cost 36

cents each and the others were 4-inch bolts that cost 42 cents each. How many 3-inch bolts did
James buy?

1 Answer

2 votes

Answer:

Amount of 3-inch bolts purchased = 18

Explanation:

We can determine the amount of 3-inch bolts James bought using a system of equations, where

  • x represents the amount of 3-inch bolts purchased,
  • and y represents the amount of 4-inch bolds purchased.

First equation:

We know that the sum of the amounts of 3-inch and 4-inch bolts equals the total amount of bolts purchased:

amount of 3-inch bolts + amount of 4-inch bolds = total amount of bolts

Since James bought 24 bolts, our first equation is given by:

x + y = 24

Second equation:

We know that the sum of the costs of the 3-inch and 4-inch bolts equals the total cost:

(price * amount of 3-inch bolts) + (price * amount of 4-inch bolts) = total cost

Since the 3-inch bolts cost $0.36 each, the 4-inch bolts cost $0.42 each, and the total cost was $9.00, our second equation is given by:

0.36x + 0.42y = 9

Method to solve: Substitution:

We can start by isolating y in the first equation:

(x + y = 24) - x

y = -x + 24

Solving for x (i.e., the number of 3-inch bolts purchased)

Now we can solve for x (i.e., the amount of 3-inch bolts purchased) by substituting y = -x + 24 in the second equation (0.36x + 0.42y = 9):

0.36x + 0.42(-x + 24) = 9

0.36x - 0.42x + 10.08 = 9

(-0.06x + 10.08 = 9) - 10.08

(-0.06x = -1.08) / -0.06

x = 18

Thus, the amount of 3-inch bolts purchased by James was 18.

Optional: Check the validity of the answer:

  • In order to check that our answer is correct, we first need to find the amount of 4-inch bolts purchased (i.e., y).

We can do this by plugging in 18 for x in the first equation (x + y = 24):

(18 + y) = 24 - 18

y = 6

Since 18 + 6 = 24, we know the solutions hold true for the first equation.

Checking the solutions in the second equation (0.36x + 0.42y = 9):

Now we can check that the solutions hold true for the second equation by plugging in 18 for x and 6 for y in 0.36x + 0.42y = 9

0.36(18) + 0.42(6) = 9

6.48 + 2.52 = 9

9 = 9

Thus, the solutions are correct.

User Riscy
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