Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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 :

Answer:

vanilla thickshake = $5

fruit juice = $3

View image rebeccarayshma

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
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.