Mixing two components at a $7.5:1$ ratio to make a solution of $200$ grams total

Question

I am mixing two components at a $7.5:1$ ratio to make a solution of $200$ grams total.

So, I tried algebra: $$200 = 7.5A + 1B\\ 200 - 1B = 7.5A\\\frac{200 - 1B}{7.5} = A.$$

How to continue from here?

Answer 1

Let the ratio of $A$ to $B$ be $7.5 : 1$ and the total weight of $A$ and $B$ be $200$ g. Then, we get the equations $200 = A + B$ and $A = 7.5B$, which means $200 = 7.5B + B = 8.5B$. Now solve for $B$ and then $A$ can be computed from one of the equations.

Answer 2

I am mixing two components at a $7.5:1$ ratio to make a solution of $200$ grams total.

So I tried algebra: $$200 = 7.5A + 1B.$$

Correction: you want $$200 = 7.5U + 1U$$ instead, because you are dividing $200$ grams among $8.5$ units so that every unit of component B goes with $7.5$ units of component A. Does this make more sense?

Answer 3

I believe ratio and proportion are taught well before linear equations in two variables, so why not use it ?

Ingredient A; (7.5/8.5)*200 gm

Ingredient B; (1/8.5)*200 gm