Question 1043905
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Let
x = amount of the juice drink that is 15% orange juice
y = amount of the juice drink that is 5% orange juice
both amounts are in liters (L)



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We have x liters from one can and y liters from another can. We mix them together and together they make 10 liters of juice. So x+y = 10 is our first equation.



We have x liters of the 15% orange juice. The amount of pure orange juice is 0.15x liters.



We have y liters of the 5% orange juice. The amount of pure orange juice is 0.05y liters.



In total, those amounts combine to 0.15x+0.05y. We want 10 liters of 7% orange juice. So we want 10*0.07 = 0.7 liters of pure orange juice.



Therefore, the two amounts must be the same (ie equal). So 0.15x+0.05y = 0.7 is the second equation



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To summarize so far, we have these two equations



x+y = 10
0.15x+0.05y = 0.7



Let's focus on the first equation for now. Solve for y to get...



x+y = 10



x+y-x = 10-x ... subtract x from both sides



y = 10-x



Now that y is isolated, we can plug this into the other equation



0.15x+0.05y = 0.7



0.15x+0.05( y ) = 0.7



0.15x+0.05( 10-x ) = 0.7 ... replace y with 10-x. Now solve for x.



0.15x+0.05(10)+0.05(-x) = 0.7



0.15x+0.5-0.05x = 0.7



0.10x+0.5 = 0.7



0.10x+0.5-0.5 = 0.7-0.5



0.10x = 0.2



0.10x/0.10 = 0.2/0.10



x = 2



We finally know the value of x. Use this to find y.



y = 10-x



y = 10-2 ... replace x with 2



y = 8



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In the end, we found that x = 2 and y = 8. Recall that at the very top we stated that


x = amount of the juice drink that is 15% orange juice
y = amount of the juice drink that is 5% orange juice



so this means that we must mix <font color=red size=4>2 liters</font> of the 15% juice drink with <font color=red size=4>8 liters</font> of the 5% juice drink.
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