Answer:
Equation is \(0.5 \text{ gal }\times(0.1)+ x\text{ gal }\times (0.35)=(0.5 + x)\times (0.15)\)
0.125 gallons of the 35% acid solution Eli should add.
Step-by-step explanation:
Given : Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution.
To find : Equation can you use to determine how many gallons of the 35% acid solution Eli should add?
Solution :
Let x be the gallons of the 35% acid solution.
According to question,
For 0.5 gallon of a 10% acid solution = \(0.5\times 0.1\)
For x gallon of a 35% acid solution = \(x\times 0.35\)
For (0.5+x) gallon of a 15% acid solution = \(0.5+x\times 0.15\)
The equation form is
\(0.5 \text{ gal }\times(0.1)+ x \text{ gal }\times(0.35)= (0.5+x)\times (0.15)\)
Solving the above equation,
\(0.05+0.35x = 0.075 + 0.15x\)
\(0.2x = 0.025\)
\(x =\frac{0.025}{0.2}\)
\(x=0.125\)
Therefore, 0.125 gallons of the 35% acid solution Eli should add.
The equation is \(0.5 \text{ gal }\times(0.1) + x \text{ gal }\times(0.35) =(0.5 + x)\times (0.15)\)
