Question

A vanilla thickshake is $2 more than a fruit juice. If 3 vanilla thickshakes and 5 fruit juices cost $30, determine their individual prices using simultaneous elimination

Answer 1

USING ELIMINATION METHOD

Let the price of vanilla thickshake = x

Let the price of fruit juice = y

Given that a vanilla thickshake is $2 more than a fruit juice.

so

• x = 2+y       ...... (Equation 1)

Given that If 3 vanilla thickshakes and 5 fruit juices cost $30.

• 3x+5y=30  ...... (Equation 2)

So the system of equations

$x = 2+y$

$3x+5y = 30$

Arrange equation variables for elimination

$\begin{bmatrix}x-y=2\\ 3x+5y=30\end{bmatrix}$

$\mathrm{Multiply\:}x-y=2\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:3x-3y=6$

$\begin{bmatrix}3x-3y=6\\ 3x+5y=30\end{bmatrix}$

so

$3x+5y=30$

$-$

$\underline{3x-3y=6}$

$8y=24$

so the system of equations becomes

$\begin{bmatrix}3x-3y=6\\ 8y=24\end{bmatrix}$

solve 8y = 24 for y

$8y=24$

Divide both sides by 2

$\frac{8y}{8}=\frac{24}{8}$

$y=3$

$\mathrm{For\:}3x-3y=6\mathrm{\:plug\:in\:}y=3$

$3x-3\cdot \:3=6$

$3x-9=6$

$3x=15$

Divide both sides by 3

$\frac{3x}{3}=\frac{15}{3}$

$x=5$

Therefore,

• The price of fruit juice = y = 3

• The price of vanilla thickshake = x = 5

             

                                              2ND METHOD

Step-by-step explanation:

• Let the price of fruit juice = x

As a vanilla thickshake is $2 more than a fruit juice.

• Thus the price of thickshake vanilla = x+2

Given that 3 vanilla thickshakes and 5 fruit juices cost $30.

3(Vanilla thickshakes) + 5(fruit juice) = 30

3(x+2) + 5x = 30

3x+6+5x=30

8x+6=30

8x=30-6

8x=24

x = 3

Thus,

• The price of fruit juice = x = $3

• The price of vanilla thickshake = x+2 = 3+2 =  $5

Answer 2

Answer:

vanilla thickshake = $5

fruit juice = $3