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3 years ago

The sum of two consecutive mile markers on the interstate is 417417. Find the numbers on the markers

Mathematics

1 answer:

noname [10]3 years ago

5 0

Hello from MrBillDoesMath!

Answer:

The first marker is labeled 208708; the second (consecutive) one 208709

Discussion:

Call the first mile marker "m". Then

m + (m+1) = 417417 => combine like terms

2m + 1 = 417417 => subtract 1 from both sides

2m = 417416 => divide both sides by 2

m = 417416/2 = 208708

Note: m and (m+1) are consecutive as they immediately follow each other in the set of integers.

Thank you,

MrB

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How many solutions does the equation x_1 +x_2+x_3+x_4+x_5=21 have where x_1, x_2, x_3, x_4, and x_5 are nonnegative integers and

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Step-by-step explanation:

$x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 21\\$ (given)

Let us consider :

$x_{1}$ = $t_{1} + 1$

$x_{2}$ = $t_{2}$

$x_{3}$ = $t_{3}$

$x_{4}$ = $t_{4}$

$x_{5}$ = $t_{5}$

Now, by substituting the above considerations in the above equation, we get:

$t_{1} + 1 + t_{2} + t_{3} + t_{4} + t_{5} = 21\\$

$t_{1} + t_{2} + t_{3} + t_{4} + t_{5} = 20\\$

where,

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then it follows

n = 20

r = 4

then no. of solutions for the eqn = $_{r}^{n + r}\textrm{C}$

= $_{4}^{24}\textrm{C}$

= 10626

Answer :

no. of solutions for the eqn 10626

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