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balu736 [363]
3 years ago
13

Is it possible to place 158 books on three shelves so that the first shelf has 8 less books than the second and 5 more books tha

n the third shelf?
Mathematics
1 answer:
Lisa [10]3 years ago
5 0
Let
x-----------------> books in <span>the first shelf
</span>y-----------------> books in the second shelf
z-----------------> books in the third shelf
we know that
x+y+z=158-------------> equation (1)
x=y-8---------> y=x+8 ------->  equation (2)
x=z+5--------> z=x-5  --------> equation (3)
<span>
 substitute (2) and (3) in (1)
</span>x+(x+8)+(x-5)=158--------> 3x=155----------> x=51.7


<span>the number of books in the first shelf (x=51.7) is not a whole number
therefore

the answer is
Is not possible to place the amount of 158 books in the amounts indicated in the problem</span>



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Step-by-step explanation:

Step 1; Assume y is the gallons in the tank while x is the range of the car. We need to determine the equation relating the y to the x values in the given coordinates. x is the dependent value whereas y is the independent value i.e. the value of x depends on the value of y.

Step 2; As y increases, x also increases. For every extra gallon in the tank, the car can go another 17 miles. So with y as the amount of gas in the tank in gallons and x as the range of vehicle, we get;

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To find the gallons in the tank, y = \frac{x}{17},

For x = 170, y = \frac{170}{17} = 10,

Similarly equating the values we get that when x = 187, y = 11,

when x = 204, y = 12,

when x = 221, y = 13,

when x = 238, y = 14,

when x = 255, y = 15,

when x = 272, y = 16,

when x = 289, y = 17,

when x = 306, y = 18,

when x = 323, y = 19,

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Step-by-step explanation:

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