This is a problem of
fact families, but <em>what is fact families?</em> Well it is a family of four things. Two of them are additions and two of them are subtractions. So this question asks about fact families by w<span>riting the <em>subtraction fact two ways</em>. So we have:
</span><span>
First way. So let's take the number 10 and explain this problem using triangles. Let's say that we have 10 triangles in the beginning:
</span>Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ
So I want to take away 3 triangles, then by taking away 3<em> what is left? </em>Well the answer is 7:
Δ Δ Δ Δ Δ
Δ Δ
That is, if we subtract 3 from 10 then the result is:
Second way. In this subtraction we take the same 10 triangles:
Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ
Now I want to take away 7 triangles, then by taking away 7 what is left is 3:
Δ Δ Δ
That is, if we subtract 7 from 10 then the result is:
Y = 7/3 or 2.33333333
y = 3x - 7
+7. +7
——————
7y =3x
—. —
3. 3
y = 7/3 or 2.3333333
So, how much acid is there in 6 gallons? well is 20% acid or (20/100), so the amount of acid in it just (20/100) * 6 or 1.2, the rest is say water.
now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.
now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.
we know whatever "x" and "y" amounts are, they -> x + 6 = y
and we also know that x + 1.2 = 0.9y
Answer:
x=7
Step-by-step explanation:
Add 16 to both sides
-17x-16+16=-135+16
Simplify
-17x=-119
Divide both sides by -17
-17x/-17=-119/-17
Simplify
x=7
Hope this helped! :)