Answer:
Initially, we had:
100 grams of a mixture that is 80% seed, (or 0.8 in decimal form)
This means that the quotient between the mass of seeds and the total mass of the mixture is equal to 0.8
Then the mass of seeds, x, can be calculated as:
x/100g = 0.8
x = 0.8*100g
x = 80g
We also have another mixture, that is 5% seed (or 0.05 in decimal form)
This means that in X grams of this mixture, there will be y grams of seeds, such that:
y/X = 0.05
y = 0.05*X grams
Now, we want to create a mixture that is 40% seeds (or 0.4 in decimal form).
Let's do this.
If we add X grams of the 5% mixture, the total mass will be:
M = 100g + X.
The total mass of seeds will be:
m = 80g + X*0.05
and we want that the quotient between the mass of seeds and the total mass to be exactly 0.4
m/M = 0.4
(80g + X*0.05)/(100g + X) = 0.4
Let's solve this for X.
(80g + X*0.05) = 0.4*(100g + X)
80g + X*0.05 = 40g + X*0.4
80g - 40g = X*0.4 - X*0.05
40g = X*0.35
40g/0.35 = X = 114.2g
If we want the mixture to be exactly 40% seeds, we need to add 114.2g of the 5% mixture. (We already can see that Tom is closer to the exact result than Sally)
If we add 114g, like Tom wants, we will have:
M = 100g + 114g = 214g
m = 80g + 0.05*114g = 85.7g
m/M = 85.7g/214g = 0.4005
This is a really good aproximation, if we write this in percentage form this would be:
0.4005*100% = 40.05%
