Question

Can somebody tell me the answer worth 50 points!!!

Answer 1

Two blue = 6

Explanation:

Let r = red

Let b = blue

2r + r + b = 21

r - b = 3 Can we rewritten r = 3 + b Substitute 3 + b for r into the first equation

2r + r + b = 21

2(3 + b) + 3 + b + b = 21 Distribute the 2

6 + 2b + 3 + b + b = 21 Combine like terms

9 + 4b = 21 Subtract 9 from both sides

9 - 9 + 4b = 21 - 9

4b = 12 Divide both sides by 4

`(4b)/(4)` =
`(12)/(4)`

b = 3

2 blues would equal 6.

Answer 2

6

Explanation:

Define the variables:

• Let x = red pencil
• Let y = blue pencil

From the given blackboard, create a system of equations from the first three equations:

`\begin{cases}3x + y = 21\\\;\:x - y = 3\\2x + y = 15\end{cases}`

Add the first equation to the second equation to eliminate y:

`\begin{array}{lrcccr}& 3x & + & y & = & 21\\+ & (x & - & y & = & 3\\\cline{2-6} &4x &&&=&24\end{array}`

Solve the equation for x:

`\implies (4x)/(4)=(24)/(4)`

`\implies x=6`

Substitute the found value of x into the second equation and solve for y:

`\implies 6-y=3`

`\implies y=3`

Therefore, the value of the red pencil is 6 and the value of the blue pencil is 3.

Finally, substitute the found value of y into the last equation:

`\implies 3 + 3 = \boxed{6}`