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Delicious77 [7]
3 years ago
11

A father decided to give twenty five percent of his monthly income to his three children as their monthly allowance. The eldest

child got forty five percent of the allowance and the youngest got twenty percent. How much is the monthly allowance given to the children if the second child got three thousand five hundred dollars?
Mathematics
1 answer:
Nastasia [14]3 years ago
3 0

Let x = father's monthly income.

.25x is split among his three children

Oldest received .45(.25x), middle child received .35(.25x), and youngest received .25(.25x).

.25(.25x) = 3500

.0625x = 3500

x = $56,000

56,000(.25) = $14,000 per month

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check the picture below.

now, we're assuming the trapezoid is an isosceles trapezoid, namely AD = BC, and therefore the triangles are twins.

incidentally, b is the height of the trapezoid and likewise is also the altitude or height of the concrete triangle.

so we can simply get the area o the trapezoid, notice the bottom base is a+185+a, and then get the area of the concrete triangle and subtract the triangle from the trapezoid, what's leftover is just the vegetation area.

\bf \begin{cases} a=283\cdot cos(80^o)\\ a\approx 49.14\\ --------\\ b=283\cdot sin(80^o)\\ b\approx 278.70 \end{cases}\\\\ -------------------------------\\\\ \textit{area of a trapezoid}\\\\ A=\cfrac{h(x+y)}{2}~~ \begin{cases} x,y=\stackrel{bases}{parallel~sides}\\ h=height\\ ----------\\ x=185\\ y\approx \stackrel{a+185+a}{283.28}\\ h\approx\stackrel{b}{278.70} \end{cases} \\\\\\ A=\cfrac{278.70(185+283.28)}{2}\implies A\approx 65254.818

so that's the area of the trapezoid, now let's get the area of the triangle.

\bf \stackrel{triangle}{\cfrac{1}{2}(185)(b)}\implies \cfrac{1}{2}(185)(278.70)\qquad \approx 25779.80\\\\ -------------------------------\\\\ \stackrel{\textit{area for vegetation}}{\stackrel{\textit{area of trapezoid}}{65254.818}~~-~~\stackrel{\textit{area of triangle}}{25779.80}}\implies 39475.018

since we know 36 yd² cost 12 bucks, then how much will it be for 39475.018 yd²?

\bf \begin{array}{ccll} yd^2&\$\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 36&12\\ 39475.018&x \end{array}\implies \cfrac{36}{39475.018}=\cfrac{12}{x}\implies x=\cfrac{39475.018\cdot 12}{36} \\\\\\ x\approx 13158.339\overline{3}

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