This week Bob puts gas in his truck when the tank was about half empty. Five days later, Bob puts gas again when the tank was about three fourths full. If Bob bought 24 gallons of gas, how many gallons does the tank hold?
half tank plus quarter tank equals three-quarters tank
3/4 t = 24 ... t = ?
It's 32 gallons:
1/2x + 1/4x = 24 gallons
The 1/2x represents the empty part on the first time. Five days later, his tank is 3/4ths filled, which means there was still 1/4ths of the tank left to be filled, so that's why I put 1/4x. I added them together in order to get the total amount of space filled, and since he used 24 gallons total, yeah...
So the result would be 3/4x=24 gallons. That means that 3/4 of the tank is 24, but your'e trying to find the whole tank, so you do 24 divided by 3/4 to get 32 gallons. Okay bye.
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Let x be total volume of can
1/2x + 1/4x = 24 gallons (We’re finding total volume of can in litres)
Now, add 1/2 and 1/4 LCM - 4 = 2/4 + 1/4 = 3/4
3/4x = 24
X = 24 / 3/4 (Transpose)
X = 24 / 3/4 (Divide) = 24 * 4/3 (Reciprocal) = 96/3 = 32 (Simplify)
So now we have the total of the volume of the container = 32
Well, we need to multiply the number of gallons to the half-filled tank to make it complete. Additionally, the 3/4 filled tank will be filled with whatever is left after adding the extra 1/2 gas. The total is 24. Hence, our mathematical statement would be:
1/2x + (3/4 - 1/2x) = 24
-x + 3/4 = 24
-x = 24 x 4/3
-x = 24 x 4/3
-x = 96/3
-x = 32
-x ( -x ) = x
Therefore, the tank holds 32 gallons! Therefore, we would have:
32/24 = 1.33...
Approximately one filled gallon using the 24 we have.
In conclusion, the tank holds 32 gallons.
The question asks us to find the total capacity of the tank. The fractions tell us that a quarter of the tank added by half the tanks is 24 gallons. So x= the total capacity and we can plug everything in.
the algebraic equation would be:
1/4x + 1/2x = 24
add the fractions together:
6/8x = 24
then we isolate the x by multiplying both sides by 8 then we divide both sides by 6:
6/8x X 8 = 24 X 8
6x = 192
6x/6 = 192/6
x = 32
To find out how many gallons the tank holds, we can subtract the amount of gas Bob bought from the initial level of the tank before he put gas in.
1. Let's assume 'x' represents the number of gallons the tank can hold.
2. Bob put gas in his truck when the tank was about half empty, which means there were x/2 gallons of gas left in the tank.
3. Five days later, when Bob put gas again, the tank was about three-fourths full, which means there were (3/4)x gallons of gas in the tank.
4. Bob bought 24 gallons of gas. Therefore, we can set up the equation: (3/4)x - (x/2) = 24.
5. To solve the equation, let's get rid of the denominators. Multiply the entire equation by 4*2 = 8 to eliminate the fractions: 8 * (3/4)x - 8 * (1/2)x = 8 * 24.
Simplifying, we get: 6x - 4x = 192.
6. Combining like terms, we have: 2x = 192.
7. Divide both sides of the equation by 2 to isolate 'x': 2x / 2 = 192 / 2.
Simplifying further, we find: x = 96.
Therefore, the tank holds 96 gallons.