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
[tex]x = 2+y[/tex]
[tex]3x+5y = 30[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}x-y=2\\ 3x+5y=30\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}x-y=2\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:3x-3y=6[/tex]
[tex]\begin{bmatrix}3x-3y=6\\ 3x+5y=30\end{bmatrix}[/tex]
so
[tex]3x+5y=30[/tex]
[tex]-[/tex]
[tex]\underline{3x-3y=6}[/tex]
[tex]8y=24[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}3x-3y=6\\ 8y=24\end{bmatrix}[/tex]
solve 8y = 24 for y
[tex]8y=24[/tex]
Divide both sides by 2
[tex]\frac{8y}{8}=\frac{24}{8}[/tex]
[tex]y=3[/tex]
[tex]\mathrm{For\:}3x-3y=6\mathrm{\:plug\:in\:}y=3[/tex]
[tex]3x-3\cdot \:3=6[/tex]
[tex]3x-9=6[/tex]
[tex]3x=15[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]
[tex]x=5[/tex]
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
