We have an algebraic problem about proportions of solutions. We will find that the nurse needs to use 550 cm^3 of the 10% solution.
We know that the nurse mixes 50cm^3 of 70% saline solution with a volume V of a 10% saline solution, such that the end product would be 15% saline solution.
We need to find the value of V.
The total amount of salt in each solution is given by the product between the volume and the percent of salt in it (written as a decimal, for example, 70% would be 0.7)
Then we have:
50cm^3*0.7 + V*0.1 = (50cm^3 + V)*0.15
Above says that the salt of the mix must be equal to the salt in a 15% solution with a volume of (50cm^3 + V)
Now we just need to solve this for V.
50cm^3*0.7 + V*0.1 = (50cm^3 + V)*0.15
50cm^3*0.7 + V*0.1 = 50cm^3*0.15 + V*0.15
50cm^3*0.7 - 50cm^3*0.15 = V*0.15 - V*0.1
27.5 cm^3 = V*(0.15 - 0.1) = V*0.05
(27.5 cm^3)/0.05 = V = 550 cm^3
The nurse needs to use 550 cm^3
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