Suppose you work in a lab. You need a 15% acid solution for a certain test, but

Question

Suppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution to make your own 15% solution. You need 10 liters of the 15% acid. How many liters of 10% solution and 30% solution should you use? Set up the systems of equation and solve. Suppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution to make your own 15% solution. You need 10 liters of the 15% acid. How many liters of 10% solution and 30% solution should you use? Set up the systems of equation and solve.

Explanation / Answer

suppose x litre of 10% solution and y litre of 30% solution are taken to make 10 litre of 15% solution

so,

for solute

x*10% + y*30% = 10*15%

for solvent

x*(100-10)% + y*(100-30)% = 10*(100-15)%

after simplification

0.1*x + 0.3*y = 1.5 equation 1st

0.9x + 0.7*y = 8.5 equation 2nd

30*(equation 2nd) - 70*(equation 1st)

27x - 7x = 85*3 - 15*7

x = (255 - 105)/20

x = 7.5 litre

using equation 1st

0.1 * 7.5 + 0.3*y = 1.5

3y = 7.5

y = 2.5 litre

x = 7.5 litre , y = 2.5 litre (answer)

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