Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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

View image rebeccarayshma
absor201

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
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.