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The royal fruit company produces two type of fruit drinks. The first type is 70% pure fruit juice , and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 80% pure fruit juice

Respuesta :

calculista

Answer:

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

Step-by-step explanation:

Let

x ----> pints of pure fruit juice at 70%

y ----> pints of pure fruit juice at 95%

we know that

[tex]x+y=110[/tex] ----> [tex]x=110-y[/tex] ----> equation A

Remember that

[tex]70\%=70/100=0.70[/tex]

[tex]95\%=95/100=0.95[/tex]

[tex]80\%=80/100=0.80[/tex]

so

[tex]0.70x+0.95y=0.80(110)[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]0.70(110-y)+0.95y=0.80(110)[/tex]

solve for y

[tex]77-0.70y+0.95y=88[/tex]

[tex]0.25y=88-77[/tex]

[tex]0.25y=11[/tex]

[tex]y=44[/tex]

Find the value of x

[tex]x=110-y[/tex] ---> [tex]x=110-44=66[/tex]

therefore

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

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