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3 years ago

john worked five less than twice as many hours as Jane did how many hours did each work if together they worked 97 hours

Mathematics

2 answers:

il63 [147K]3 years ago

6 0

John worked 61 yours and Jane worked 36 hours

kompoz [17]3 years ago

6 0

<h3>Answer with Step-by-step explanation:</h3>

Let Jane worked for x hours

John worked five less than twice as many hours as Jane

i.e. John worked for 2x-5

Together they worked 97 hours

i.e. x + 2x -5 =97

i.e. 3x -5 =97

i.e. 3x = 102

i.e. x= 34

and 2x - 5= 2×34-5

= 63

Hence, Jane worked for 34 hours

and John worked for 63 hours

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<u>There are 17 terms in the sequence</u>

Step-by-step explanation:

<u>Arithmetic Sequence </u>

An arithmetic sequence is a list of numbers with a definite pattern by which each term is calculated by adding or subtracting a constant number called common difference to the previous term. If n is the number of the term, then:

$a_n=a_1+(n-1)r$

Where an is the nth term, a1 is the first term, and r is the common difference.

In the problem at hand, we are given the first term a1=13, the last term an=-23, and the common difference r=-2 1/4. Let's solve the equation for n:

$\displaystyle n=1+\frac{a_n-a_1}{r}$

We need to express r as an improper or proper fraction:

$\displaystyle r=-2\frac{1}{4}=-2-\frac{1}{4}=-\frac{9}{4}$

Substituting:

$\displaystyle n=1+\frac{-23-13}{-\frac{9}{4}}$

$\displaystyle n=1+\frac{-36}{-\frac{9}{4}}$

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