A childs ticket = $28 and an adult = $45
Total Cost to each family is the number of adult tickets bought multiplied by "x" PLUS the number of child tickets bought multiplied by "y"
Henson's equation = 3x + y = 163 Garcia's equation = 2x + 3y = 174
using the substitution method we need to express either x or y in terms of the other variable. In this example looking at the Henson equation it is very easy to express y in terms of x.
Rewrite the Henson equation to make y the subject y = 163 - 3x Substitute this value (163 - 3x) for "y" in the Garcia equation which now becomes
2x + 3(163 - 3x) = 174 Expand the bracket 2x + 489 - 9x = 174 -7x + 489 = 174 Add 7x and subtract 174 from both sides of the equation 315 = 7x 315/7 = x 45 = x An adult ticket costs $45 Substitute this back into the Henson equation 3 * 45 + y = 163 135 + y = 163 y = 163 - 135 = 28 A childs ticket costs $28
Check in the Garcia equation 2 * 45 + 3 * 28 = 90 + 84 = 174 = CORRECT
A childs ticket = $28 and an adult = $45
Answer:
5 cups
Step-by-step explanation:
1 kilogram is 1000 grams
1/2 of a kilogram is 500 grams
20% * 300 = 2 * (10% * 300) = 2*30 = 60
Since the function is continuous between x = 0 and x = 44 then Rolle's theorem applies here.
Differentiating
y' = x * 2(x - 44) + (x - 44)^2
y' = 3x^2 - 176x + 1936 = 0 (at a turning point).
solving we get x = 44 , 14.67
y" = 6x - 176 which is negative for x = 14.67 so this gives a maximum value for f(x)
This maximum is at the point (14.67, 12,619.85)
There is a minimum at ( 44,0)
These are the required points
