Which one is a basic alligation math problem? Reviewing the difference!

1. How many ml of 3% Therapeutic bath lotion is required to mix with 11% Therapeutic bath lotion to make it 7% of 750 ml Therapeutic bath lotion?

2. How many ml of a syrup containing 85% of sucrose should be mixed with 150 ml of a 60% sucrose syrup to make it a syrup containing 80% sucrose?

Read the questions carefully because these types of questions can trick you into solving incorrectly

The basic alligation problem is # 1. Here is why below:

- Question # 1 is asking how many ml's of a 3% lotion is needed to be mix with a 11% lotion to get a total of 750 ml, in other words 2 different strength lotions are being mixed together to get our final volume that was provided (750ml).

11% I I 4% parts (4% X 750ml / 8% = 375 ml)

_______I________I______

I 7% I 8% total parts

______________________

I I

3% I I 4% parts (4% X 750ml / 8% = 375 ml)

A tip to see if your answer was correct: Add both final volumes 375 ml + 375 ml = 750 ml is the total volume that was in the question, now we are sure this math question was solved correctly.

Answer: We need 375 ml of a 3% Therapeutic bath lotion

Why can't I solve question 2 with the basic alligation method?

- The question does not provide the final volume
- The question provides the first half of volume that is only going to be mixed, in other words we need to solve the second volume to equal or get our final volume that would obtain the specific %. Basically solve for the unknown ( X ), this is where algebra comes in the picture.

How many ml of a syrup containing 85% of sucrose should be mixed with 150 ml of a 60% sucrose syrup to make it a syrup containing 80% sucrose?

Do you remember to change a % to a decimal? [EX] 85% / 100 = 0.85

Step 1: 0.85x + 0.6(150ml) = 0.8 ( x + 150ml ) -------- setup algebraic equation

Step 2: 0.85x + 90 = 0.8x + 120

Step 3: 0.85x - 0.8x = .05

Step 4: 0.8x - 0.8x [cancel out to isolate x]

Step 5: 90 - 120 = 30

Step 6: 120 - 120 [cancel out]

Step 7: 30 / .05 = 600

Answer: We need 600 ml of a 85% of sucrose

Here is another example:

How many grams of 3% Salicylic acid powder is required to mix with 400 gm of 8% salicylic acid to prepare 5% salicylic acid powder?

Step 1: 0.03x + 0.08 (400gm) = 0.05 ( x + 400gm) ----------- setup algebraic equation

Step 2: 0.03x + 32 = 0.05x + 20

Step 3: 0.03x - 0.03x [ cancel out to isolate x ]

Step 4: 0 0.5x - 0.03x = .02

Step 5: 32 - 20 = 12

Step 6: 20 - 20 [ cancel out ]

Step 7: 12 / .02 = 600 gm

Answer: We need 600 gm of 3% salicylic acid

Since you learned how to solve with algebra, here is a very easy way to solve without algebra, it's always good to have a 2nd method just to be sure with our final answer. Lets use the same question above.

How many grams of 3% Salicylic acid powder is required to mix with 400 gm of 8% salicylic acid to prepare 5% salicylic acid powder?

8% 2% parts [we know 8% contains 400gm]

_____I_________I______

I 5% I

____________________

3% I I 3% parts [ unknown gm for 3%]

Do math: 400gm X 3% parts / 2% parts = 600gm

Crystal's Comment: Don't you feel relief now? lol! I showed you both of these methods because at times when solving a math problem, you are not sure if your answer was correct so now that you have 2 different methods to solve the same question it will assure you that your answer was correct.

2 Bonus questions:

1. If 0.025% of 80 grams of Triamcinolone were mixed with 0.05% of 15gms of Triamcinolone, what would be the final concentration of Triamcinolone in the resulting mixture?

NOTE: You can solve this by using algebra or with the ratio & proportion method, lets setup our algebraic equation first:

Remember from the mini algebra tutorial I said to solve equations first? Well these 2 questions are examples of that.

0.8g (0.025%) + 0.15g (0.05%)

0.8g X 0.025% = 0.02

0.15g X 0.05% = 0.0075

0.02 + 0.0075 = 0.0275 ...round

Answer: 0.028% w/w

OR

0.025g = 100gm

X = 80gm --------< 0.025g X 80gm / 100gm = 0.02gm

0.05g = 100gm

X = 15gm ----------< 0.05g X 15gm / 100gm = 0.0075gm

0.02gm + 0.0075gm = 0.0275 [round] 0.028 % w/w

2. If 1% of 30 grams of Hydrocortisone is mixed with 2.5% of 60 grams of Hydrocortisone, what is the % of hydrocortisone in final mixture?

0.01 (30g) + 0.025 (60g)

0.01 X 30g = 0.3

0.025 X 60g = 1.5

0.3 + 1.5 = 1.8 .....round

Answer: 2% w/w is the final mixture

OR

1g = 100gm

X = 30gm ------------< 1g X 30gm / 100gm = 0.3gm

2.5g = 100gm

X = 60gm -----------< 2.5g X 60gm / 100gm = 1.5gm

0.3gm + 1.5gm = 1.8 [round] 2% w/w