For this item, we let x be the amount of the white chocolate in the candy. With this representation and given that there is 3 lbs of peppermint sticks, the total mass of the candy is x+3.
Since white chocolate comprises the 75% of the candy, we make an equation that is, x / (x + 3) = 0.75 The value of x from the equation is 9 lbs.
When you are asked to find the area under the curve with a given equation, this is an application of integral calculus. The concept is that, any infinitesimal strip under the curve, when added together, equals the area. Thus, integrate the given equation with limits from 0 to 2.
A = [x³/3 - 4x]lim 0->2 A = (2³/3 - 4(2)] - (0³/3 - 4(0)] A = 16/3 - 0 A = 16/3 ≈ <em>5.3 sq. units</em>
Write equations using information from the problem
x = y - 6 "Devaughn is 6 years younger than Sydney"
x + y = 82 "The sum of their ages is 82"
Solve using the <u>substitution</u> method
Notice that the first equation equals to "x". The second equation has the letter "x". You can replace the second "x" using the expression in the first equation.
x + y = 82 Second equation. Replace "x" with y - 6.
y - 6 + y = 82 Combine like terms (add the "y"s together)