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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

Sagot :

rebeccarayshma

Answer:

vanilla thickshake = $5

fruit juice = $3

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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
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