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A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 15% real fruit juice. The company used 100.5 liters of real fruit juice to make 30 more liters of Drink A than liters of Drink B. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system

 Sep 24, 2021
 #1
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Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system. 

 

Hello Guest!

 

The volume of the fruit drink from company A is a.

The volume of the fruit drink from company B is b.

 

\(20\%a+15\%b=105l\\ \underline{a=b+30l}\)

 

\(20\%(b+30l)+15\%b=105l\\ 0.2b+0.2\cdot 30l+0.15b=105l\\ 0.35b=105l-0.2\cdot 30l\\ 0.35b=105l-6l\\0.35b=99l \)

\(b=\dfrac{99}{0.35}\cdot \dfrac{20}{20}=\dfrac{1980}{7}\)

 

\(b=282\frac{6}{7}\ l=282.\overline {857142}\ l\\ a=312\frac{6}{7}\ l=312.\overline {857142}\ l\\\)

laugh  !

 Sep 24, 2021
edited by asinus  Sep 24, 2021
 #2
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Let the the number of liters of Drink B==B
The numbers of liters of drink A ==B + 30


0.15B  +  0.20 * [B + 30] ==100.5, solve for B
0.15B  +  0.20B +  6 ==100.5
0.35B ==100.5 - 6 ==94.5


B ==94.5 / 0.35 ==270 Liters of Drink B was made
270 + 30 == 300 Liters of Drink A was made.

 Sep 24, 2021

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