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Ostrovityanka [42]
3 years ago
7

Four positive whole numbers add up to 39. One of the numbers is a Multiple of 7. The other three numbers are equal. Work out the

result when the four numbers are mutliplied.
Mathematics
1 answer:
MrMuchimi3 years ago
3 0
4 positive whole numbers add up to 39. That means there are 4 factors. One is a multiple of 7. (7,14,21,28,35) The other 3 are equal. Let X equal the multiple of 7, and let Y equal the numbers that are equal.
39=x+3y
Now, we have to fill in the possible multiples of 7.

39=7+3y
39-7=7-7+3y
32=3y
32/3=3y/3
10&2/3=y
When we use 7, the 3 numbers are not equal whole numbers. Let's try the next multiple.
39=14+3y
39-14=14-14+3y
25/3=3y/3
5=y
Yes, that is a whole positive number. It's correct.

We have to plug in the other multiples just to check, but I'll leave out the work.

39=21+3y
6=y
Yes, that is a possible answer.

39=28+3y
3&2/3=y The 3 numbers are not whole numbers.

39=35+3y
1&1/3=y The 3 numbers are not whole numbers.


In conclusion, the TWO possible answers are 39=14+3(5) and 39=21+3(6). If we multiply all four numbers for the first one then it equals 1750, and the second one equals 4536. Not sure what exactly your looking for, but I answered the best I could! Hope this helped. :)
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A certain triangle has a perimeter of 3084 mi. The shortest side measures 76 mi less than the middle side, and the longest side
kari74 [83]

shortest side: 851

middle side:927

longest side : 1306

Explanation

Step 1

Let

x represents the shortest side

y represents the middle side

z represents the longest side

so, set the equations

a) the perimeter of a rectangle is the sum of the sides, so

\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}

b) The shortest side measures 76 mi less than the middle​ side( in other words, you have to subtract 76 from middle side to get the shortest side)

x=y-76\Rightarrow equation(2)

c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)

z=y+379\Rightarrow equation(3)

Step 2

solve the equations

a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)

\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\  \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}

now, replace the y value in equatino (2) to find x

b)

\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}

c) finally, prelace x and y value in equation (1) to find z

\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}

so

shortest side: 851

middle side:927

longest side : 1306

I hope this helps you

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