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goldfiish [28.3K]
3 years ago
12

Alice, Ben and Carol shared a sum of money they received. Alice received 1/5 of the money. The rest of the money was divided bet

ween Ben and Carol in the ratio 1:3. If Carol received $6 more than Alice, how much money did Ben receive?
Mathematics
1 answer:
Levart [38]3 years ago
8 0

Answer:

$3

Step-by-step explanation:

The money shared by Ben and Carol was split ...

... Ben : Carol = 1 : 3

The difference of these ratio numbers is 2, and the difference in amount received is $6. Thus, each ratio unit must stand for $6/2 = $3.

... Ben received 1×$3 = $3

_____

<em>The Rest of the Story</em>

Carol received 3×$3 = $9. Together, Ben and Carol received $3 + 9 = $12, which is 4/5 of the total amount. Then the 1/5 of the total amount that Alice received is

... (1/5)×$12/(4/5) = (1/4)×$12 = $3.

The $15 of money was split ...

... Alice : Ben : Carol = $3 : $3 : $9

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Let's start by solving the first equation.

a) -3 = 7 + 2t/3 
To begin simplifying this equation, we should multiply both sides by 3 to get rid of the denominator on the right side of the equation.
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Next, we should subtract 7 from both sides to cancel out the 7 on the right side.
-16 = 2t
Finally, we should divide both sides by 2.
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Now let's move on to the next equation.

b) 4(5x-2) = 7(2x+3)
Let's use the distributive property to get rid of the parentheses and their coefficients.
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Now, lets subtract 14x from both sides of the equation.

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Next, let's add 8 to both sides of the equation.

6x = 29

And divide both sides by the coefficient of x, which is 6.

x = 29/6 or 4 5/6

Now for the last equation.

C) 2x - 6 = 20 - 2.5x
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4.5x - 6 = 20
Now, let's add 6 to both sides to get the variable term alone.
4.5x = 26
Finally, we should divide both sides by 4.5 to get x by itself.
x = 5 7/9

Hope this helps! :)
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