Question

Question #51f4c

Answer 1

29

Explanation:

Let’s make R stand for the Red marbles, and B for the Black.

From the info given, we can see that red has twice more than black plus 3, so `R = 2B+3`

Note that the `Total = R + B`

You want to replace R with the equation we found earlier, so:

`Total = R + B = 2B +3 +B`

And since we know the total amount of marbles, we can plug that in.

`42 = 2B + 3 + B`

Move like terms together (subtract 3 on both sides, 2B+B = 3B)

`39 = 3B`

Solve B (Divide both sides by 3)

`39/3 = (3B)/3`

`13 = B`

We have solved the amount of black marbles. There are 13 black marbles!

Now plug it back to the R equation we found earlier to get the amount of red marbles. (Equation is 2B+3.) Since we found the amount of black marbles (B), you can replace B with 13 to find R

`R = 2B+3 = 2(13) +3 = 29`

There are therefore 29 red marbles.

Answer 2

Pam has a total of `29` red marbles

Explanation:

Method 1
Let the number of black marbles be `x`.
Then the number of red marbles is `(2x+3)`

By setting up an equation,
`x+(2x+3)=42`
`3x+3=14xx3" " (div 3)`
`x+1=14`
`x=13`

Therefore, Pam has a total of `[2(13)+3]`
`=29` red marbles

Method 2
Let the number of red marbles be `x`.
Then the number of black marbles is `((x-3)/2)`

By setting up an equation,
`x+((x-3)/2)=42" "(xx2)`
`2x+x-3=84`
`3x-3=3*28" "(div3)`
`x-1=28`
`x=29`

Therefore, Pam has a total of `29` red marbles