Answer:
a) Cost of the child-care center: y = 300 + 79x
Cost of the family-run childcare: y = 180 + 93x
Where x is the number of weeks.
b) In the short-term, the family-run childcare will be cheapest because the charge for enrolling is less than for the child-care center.
c)The long term option (child-care center) becomes more cost-effective if you plan to enroll your child for more than 8.6 weeks.
Step-by-step explanation:
Hi there!
a)Let y be the cost of childcare. In the child-care center, the cost is 300 plus 79 per week. Let x be the number of weeks, then the cost function for the child-care center will be:
y = 300 + 79x
In the same way, the cost of the family-run childcare will be:
y = 180 + 93x
b) In the short-term, the family-run childcare will be cheapest because the charge for enrolling is less than for the child-care center. Let´s calculate the cost of both childcare options for low values of x:
Child-care center:
y = 300 + 79 x
x = 0, y = 300
x = 1, y = 379
x = 2, y = 458
x = 3, y = 537
x = 4, y = 616
Family-run:
y = 180 + 93x
x = 0, y = 180
x = 1, y = 273
x = 2, y = 366
x = 3, y = 459
x = 4, y = 552
c) We have to find the value of x for which the cost of the family-run childcare is greater than the cost of the child-care center:
cost family-run > child-care center
180 + 93x > 300 + 79 x
93x -79x >300 - 180
14x > 120
x > 120/14
x > 8.6
The long term option (child-care center) becomes more cost-effective if you plan to enroll your child for more than 8.6 weeks.
Answer: x = 9
Explanation:
keeping in mind that perpendicular lines have negative reciprocal slopes, hmmm what's the slope of the equation above anyway?
![\bf y = \cfrac{2}{3}x\implies y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+0\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20y%20%3D%20%5Ccfrac%7B2%7D%7B3%7Dx%5Cimplies%20y%20%3D%20%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7D%7Dx%2B0%5Cqquad%20%5Cimpliedby%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20slope-intercept~form%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y%3D%5Cunderset%7By-intercept%7D%7B%5Cstackrel%7Bslope%5Cqquad%20%7D%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7Bm%7Dx%2B%5Cunderset%7B%5Cuparrow%20%7D%7Bb%7D%7D%7D%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
so we're really looking for the equation of a line whose slope is -3/2 and runs through (0,0).
Numbers? Letters? Objects?
