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Vinvika [58]
3 years ago
8

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 number

of cans,and one shelf with only 3 cans.How many cans are on each of the equal shelves?
Mathematics
1 answer:
ICE Princess25 [194]3 years ago
6 0

Answer:

There are 8 cans on each of the equal shelves

Step-by-step explanation:

Total number of cans put in display = 35

Shelves with equal no of cans =  4 Shelves

And one shelf displays only 3 cans

Therefore, 4 shelves with equal no of cans + 1 shelf with 3 cans = 35 cans

Let us assume equal no. of cans be x

We get, 4x + 3 = 35

             4x = 35 - 3

             4x = 32

              x  = 32 ÷ 4

              x = 8

<u><em>Thus, 4 shelves with equal no of cans contains 8 cans each.</em></u>

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1. 60,30,90 right triangle. y will be hypotenuse/2, x will be
hypotenuse*sqrt(3)/2. So x = 16*sqrt(3)/2 = 8*sqrt(3), approximately 13.85640646 
y = 16/2 = 8  
2. 45,45,90 right triangle (2 legs are equal length and you have a right angle).
X and Y will be the same length and that will be hypotenuse * sqrt(2)/2. So 
x = y = 8*sqrt(2) * sqrt(2)/2 = 8*2/2 = 8 
 3. Just a right triangle with both legs of known length. Use the Pythagorean theorem 
x = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13  
4. Another right triangle with 1 leg and the hypotenuse known. Pythagorean theorem again. 
y = sqrt(1000^2 - 600^2) = sqrt(1000000 - 360000) = sqrt(640000) = 800  5. A 45,45,90 right triangle. One leg known. The other leg will have the same length as the known leg and the hypotenuse can be discovered with the Pythagorean theorem.  x = 6. y = sqrt(6^2 + 6^2) = sqrt(36+36) = sqrt(72) = sqrt(2 * 36) = 6*sqrt(2), approximately 8.485281374  
6. Another 45,45,90 triangle with the hypotenuse known. Both unknown legs will have the same length. And Pythagorean theorem will be helpful. 
x = y. 
12^2 = x^2 + y^2 
12^2 = x^2 + x^2 
12^2 = 2x^2 
144 = 2x^2 
72 = x^2 
sqrt(72) = x 
6*sqrt(2) = x 
x is approximately 8.485281374  
7. A 30,60,90 right triangle with the short leg known. The hypotenuse will be twice the length of the short leg and the remaining leg can be determined using the Pythagorean theorem. 
y = 11*2 = 22. 
x = sqrt(22^2 - 11^2) = sqrt(484 - 121) = sqrt(363) = sqrt(121 * 3) = 11*sqrt(3). Approximately 19.05255888  
8. A 30,60,90 right triangle with long leg known. Can either have fact that in that triangle, the legs have the ratio of 1:sqrt(3):2, or you can use the Pythagorean theorem. In this case, I'll use the 1:2 ratio between the unknown leg and the hypotenuse along with the Pythagorean theorem. 
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y^2 = (2y)^2 - (22.5*sqrt(3))^2 
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y = sqrt(2025/4) = sqrt(2025)/sqrt(4) = 45/2 
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 x = 2*y = 2*22.5 = 45  
9. Just a generic right triangle with 2 known legs. Use the Pythagorean theorem. 
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10. Another right triangle, another use of the Pythagorean theorem. 
x = sqrt(50^2 - 14^2) = sqrt(2500 - 196) = sqrt(2304) = 48
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