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Answer:
The answer is 25 :)
Step-by-step explanation:
Ok, this explanation will probably be super confusing so sorry about that but you get two statements about each aquarium. Aquarium 1 starts with 4.6 gallons and will INCREASE by 1.2 gallons every minute. So now you have statement one, so let's plug it into the y=mx+b formula. y is the result/ the answer you get, m is the slope/how much your points INCREASE or DECREASE. x is the variable you use to plug and b is your starting point. So you are trying to find the y which means we cannot plug it in yet so right now we have y=mx+b. your next letter to switch out is m. Like I said, M is how much each point increases or decreases and if you go back, the statement says "will increase by 1.2 gallons every minute." so your m is 1.2 and will be positive because of the keyword INCREASE. now we have y=1.2x+b. B is your starting point so let's go back to the statement to find the starting point/ number, it states "Aquarium 1 contains 4.6 gallons" meaning aquarium 1 starts with 4.6 gallons, so let's plug it into the equation. you should have y=1.2x+4.6, which is your first equation. Your next equation will be a bit more tricky. we start with y=mx+b and we start with finding m, how much each point will increase or decrease. "Isaac will begin DRAINING aquarium 2 at a rate of 0.8 gallon per every minute." so M will be .8 but notice the keywords DRAINING, meaning decreasing. So because Isaac isn't filling and increasing, but he is decreasing, you will make .8 negative. so you should currently have y=-.8x+b. Now let's find the starting point, or B. "Aquarium 2 contains 54.6 gallons of water." making your m 54.6 gallons of water. Let's plug it in. y=-.8x+54.6. Now that you have to equations, this is how you will find when both equations have a point intercepting, or in other words, the answer you are looking for. you will remove the "y=" on both equations, and place an "=" between them. You should have something looking like this on your paper. "1.2x+4.6 = -.8x+54.6". Now you are going to combine like terms, so look on both sides of the equation and look for the 2 numbers with no "x" next to them. You should find "4.6" on your left and "54.6" on your right side of the equal sign. you are going to equal out "4.6" with itself by writing "-4.6" underneath it but because you did this on one side of the equal sign, you have to do it on the other side but before you do so you should have "1.2x = -.8x+54.6". now let's subtract "4.6" to "54.6" you will write "-4.6" underneath "54.6" to get your new number, "50". your problem should look like "1.2x = -.8x + 50". now we are going to do the same for your number's with an "x" by it. on the right side of the equation, you will cancel out "-.8x". notice it's NEGATIVE so, in order to cancel out a negative number, you just make the number positive. so you will ADD ".8x" to "-.8" to get 0 but because you added ".8x" to one side, you have to do it to the other side. Let's check what we have first, you should have "1.2x = 50". so now let's ADD ".8x" to "1.2x". you will get "2x" so now you should have both equations simplified like this, "2x = 50" and now we are going to make x one so we will divide "2x" by "2" to get "x", but because you did this to one side, you have to do it to the other. so now you divide "50" by "2" to get 25. now you should have written down "x = 25". Thank you so much for reading this and please let me know if this was helpful or confusing. :)))
The time at which both aquariums contain the same amount of water is 25 minutes and this can be determined by forming the linear equation.
Given :
- Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute.
- Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallons per minute.
The following steps can be used in order to determine the time at which both aquariums contain the same amount of water:
Step 1 - Let the time be 't' at which both aquariums contain the same amount of water.
Step 2 - The amount of water in the Aquarium I at time 't' is given by:
V = 4.6 + 1.2t
where V is the total amount of water at time 't'.
Step 3 - The amount of water in the Aquarium II at time 't' is given by:
V' = 54.6 - 0.8t
where V' is the total amount of water at time 't'.
Step 4 - So, time at which both aquariums contain the same amount of water is given by:
V = V'
4.6 + 1.2t = 54.6 - 0.8t
Step 5 - Simplify the above equation.
50 = 2t
t = 25 minutes
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/11897796
