This is a multi-step problem, and I am lost: These are the previous steps: Step 1 We are given that Kevin can stuff 1,550 shrimp in 6 hours, so he can stuff  1550 6    6  shrimp...

This is a multi-step problem, and I am lost:

These are the previous steps:

Step 1
We are given that Kevin can stuff 1,550 shrimp in 6 hours, so he can stuff 
1550 6   

6

 shrimp per hour. Let x be the number of hours it takes his his sister to stuff 1,550 shrimp. This definition of x will simplify the calculation. To get the time it takes to stuff 775 shrimp, divide   

divide

 the value of xby 2. Her stuffing rate is 
129.15   

1550

x
 shrimp per hour.
Step 2
We are given that Kevin and his sister together can stuff 1,550 shrimp in 4 hours, so their combined rates add up to the following.
  Kevin's rate     plus     His sister's rate     equals     Their combined rate     1550 6  +  1550 x  =  1550 4   

4

I do not understand what they are talking about:

We solve this equation for x. Multiply both sides by the LCD of the three fractions, 12x, and simplify.

3100x + 18600 =  x


Subtract 3100x from both sides.

18600 =  x


Divide both sides of the equation by the coefficient of x.

 = x

Asked on by suscausey

1 Answer | Add Yours

violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

For step `1` note that:
amount of work = rate * time

Therefore, rate = amount of work/time

Since Kevin can stuff `1,550` shrimp in `6` hours the amount of work is `1,550` and the time is `6` , hence his rate is `1550/6` .

For the step `2` , we will apply the same formula. This time we do not know the time it takes her sister to stuff `1,550` shrimp, so we let it as x. So, the rate of her sister is `1550/x` .

For step` 3` , since we know that they can stuff `1,550` shrimp in `4` hours together the combine rate is `1550/4` . We will apply addition since we are ''combining'' rates.

Take the sum of the rates of Kevin and her sister.

`1550/6 + 1550/x = 1550/4`

Identify the LCD.
The denominators are `6` , `x` , and` 4` . Since there is a variable `x ` we will include it on the LCD.
Take the lcm (least common multiple) of `6` and `4` .
The multiples of` 6 ` are: `6,12,18, 24, 30, 36, 42, 48, 54, 60` .
The multiples of `4` are:` 4, 8, 12, 16, 20, 24, 28, 32, 36, 40` .
Therefore, the LCM is `12` . Therefore the LCD is `12 * x = 12x` .
To get rid of the denominators we multiply both sides by the LCD.

`(12x)*(1550)/(6) + (12x)*(1550)/(x) = (12x)*(1550)/(4)`  

Simplifying `12/6 = 2` ,` (12x)/(x) = 12 ` and `(12x)/(4) = 3` .

`(2x*1550) + (12*1550)=(3*1550)`

`3100x + 18600 = 4650x`

Since, we are solving for `x` we put the terms with` x` on one side. So, we need to move the` 3100x ` to the right side. Since `3100x ` is being added on left side, we use the opposite operation of addition which is subtraction. So, subtract` 3100x` on both sides.

`3100x + 18600 -3100x = 4650x - 3100x`

`18600 = 1550x`

Isolate the `x` on right side by dividing `1550` on both sides.

`(18600)/(1550) = (1550x)/(1550)`

`12 = x` or `x = 12`

Therefore, the time it takes for Kevin's sister to stuff `1550` shrimp is `12` hours.

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Also, remember that the original question is to find the amount of time the sister takes to prepare 775 shrimp. You have found the time to do 1550 shrimp (12 hours), so the time to do 775 shrimp is 1/2 this or 6 hours. (Hence the hint in step 1 to find x and divide by 2.)

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