Answers:
She made ___25___ grams of ___40___% salt solution
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The given info "20 grams of 50% salt solution" tells us that we have 10 grams of pure salt
Since 50% of 20 = 0.50*20 = 10
Put another way, we have 10 grams of pure salt out of 20 total so 10/20 = 0.50 = 50% salt solution
The 20 grams of solution updates to 25 grams of solution when we add the 5 grams of water
We don't add any salt, assuming this water is fresh water
So we still have 10 grams of pure salt out of 25 grams now
10/25 = 2/5 = 0.40 = 40% is the new salt concentration
Okay. So 90 yds was cut from the 230 yd yarn. 230 - 90 = 140. 1/2 of 140 is 70. 230 - 70 = 160. The yellow yarn was 160 yds longer than the blue yarn at first.
B is just the y-intercept or where the line goes over the y axis so it would be 50
Y = mx + b
First equation 1 = m(4) + b, bring everything to one side m(4) + b - 1 = 0
Second equation 7 = m(5) + b, bring everything to one side m(5) + b - 7 = 0
Set them equal to each other,
m(4) + b - 1 = m(5) + b - 7
If you bring the b over to the left hand side it becomes
m(4) + b - b - 1 = m(5) - 7
m(4) - 1 = m(5) - 7
Solve for m
6 = m
Plug m = 6 into either equation from the beginning,
m(4) + b - 1 = 0
6(4) + b - 1 = 0
24 + b - 1 = 0
b = -23
Knowing m and b we can now make an equation
y = mx + b
y = 6x -23 Final answer
