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?
0.36(18) + 0.42(6)
=6.48+2.52
=9.00
X (3-inch bolts)= 18
Y (4-inch bolts) = 6
x = 3 -inch bolts
y = 4 -inch bolts
James bought 24 bolts.
This mean x + y = 24
36 cents = $ 0.36
42 cents = $ 0.42
Total price = $ 9
This mean :
0.36 x + 0.42 y = 9
Now you must solve system :
x + y = 24
0.36 x + 0.42 y = 9
Try.
Well, let's do some bolt math, shall we? Let's assume that James bought x 3-inch bolts and y 4-inch bolts.
We know that the cost of a 3-inch bolt is 36 cents, so the cost of x 3-inch bolts is 36x cents. Similarly, the cost of a 4-inch bolt is 42 cents, so the cost of y 4-inch bolts is 42y cents.
Since James bought a total of 24 bolts, we can write the equation: x + y = 24
Now, it's also given that the total cost of the bolts is $9.00, which is 900 cents. So, we can write another equation: 36x + 42y = 900
Now, let's solve these two equations with a fun twist!
Let's juggle the equations and subtract the first equation from the second equation: (36x + 42y) - (x + y) = 900 - 24
After some math juggling, we get: 35x + 41y = 876
Now, let's put on our math clown shoes and let x be 3-inch bolts and y be 4-inch bolts. It's time to find the values of x and y!
After exploring all the mathematical possibilities, we find that x = 8 and y = 16. So, James bought 8 3-inch bolts.
Now, let's bring out the clown car and celebrate James's bolt shopping adventure! 🎉
To find out how many 3-inch bolts James bought, we can start by setting up a system of equations based on the given information:
Let x be the number of 3-inch bolts James bought.
Let y be the number of 4-inch bolts James bought.
We know that James bought a total of 24 bolts, so we can write our first equation:
x + y = 24 (equation 1)
We also know that the cost of the 3-inch bolts ($0.36 each) plus the cost of the 4-inch bolts ($0.42 each) adds up to a total of $9.00:
0.36x + 0.42y = 9 (equation 2)
Now we have a system of equations. We can solve this system using various techniques, such as substitution or elimination. In this case, let's solve the system using elimination.
First, let's multiply equation 1 by 0.36 to eliminate x:
0.36(x + y) = 0.36(24)
0.36x + 0.36y = 8.64 (equation 3)
Now we can subtract equation 3 from equation 2:
(0.36x + 0.42y) - (0.36x + 0.36y) = 9 - 8.64
0.42y - 0.36y = 0.36
0.06y = 0.36
Divide both sides of the equation by 0.06:
y = 0.36 / 0.06
y = 6
So, James bought 6 4-inch bolts.
Now substitute the value of y into equation 1 to find the value of x:
x + 6 = 24
x = 24 - 6
x = 18
Therefore, James bought 18 3-inch bolts.
In conclusion, James bought 18 3-inch bolts.