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3 years ago

The larger of two numbers is four more than the smaller number.If the sum of the numbers is 61,find the numbers

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

6 0

Answer:

<u>28.5 and 32.5</u>

Step-by-step explanation:

<em>create an equation to solve:</em>

x + (x+4) =61

2x + 4 = 61 combine like terms

2x = 57 subtract 4 from both sides

x = 28.5 divide 2 from both sides

28.5 is the smaller number

the larger number is 4 more so:

28.5 + 4 = 32.5

32.5 is the larger number

check your work:

28.5 + 32.5 = 61

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Answer:

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Step-by-step explanation:

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Strike441 [17]

Answer:

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Step-by-step explanation:

We are given the arithmetic sequence:

$\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots$

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Find the common difference by subtracting the first term from the second:

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The common difference is (7<em>x</em> + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

$\displaystyle x_n = a + d(n-1)$

Where <em>a</em> is the initial term and <em>d</em> is the common difference.

The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:

$\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)$

To find the 13th term, let <em>n</em> = 13. Hence:

$\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)$

Simplify:

$\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}$

The 13th term is 81<em>x</em> + 59.

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