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user100 [1]
3 years ago
7

Ari stocks shelves at a grocery store. He puts 35 cans of juice in each display case. The case has 4 shelves with an equal numbe

r of cans, and one shelf with only 3 cans. How many cans are on each of the equal shelves?
Mathematics
2 answers:
Umnica [9.8K]3 years ago
8 0
Well let's see. First, the equation is 35-3÷4.
So 35-3 is 32.
And 32÷4 is 8.
There are 8 cans on each equal shelves.
Tamiku [17]3 years ago
5 0
In one display case there are 5 shelves in it. It was said that 4 shelves stores equal number of juice cans in it while the other one has only 3 cans. As a whole, Ari has 35 cans of juice. By placing 3 in one of the shelves, we can deduct it from 35 or (35 minus 3) so what we now have is 32 pieces of juice cans left to be equally distributed in the 4 shelves left. The equation will now be 32 divided 4 or 32/4 which will be equal to 8. So in each shelf from the 4 shelves will store 8 cans of juice equally. 
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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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