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VashaNatasha [74]

3 years ago

9

A carpenter has less than 120 min. to spend painting furniture each day. Today, he has spent 30.5 min. painting a desk. Now he w

ill paint x chairs, each of which takes 12.5 min.
What is the maximum number of chairs the carpenter can paint?

A, 7
B, 8
C, 12
D, 13

2 answers:

FinnZ [79.3K]3 years ago

6 0

Answer:

Hence, a carpenter can paint a maximum of 7 chairs.

Hence, option A is correct.

Step-by-step explanation:

A carpenter has less than 120 min. to spend painting furniture each day.

Today, he has spent 30.5 min. painting a desk.

Now he will paint x chairs, each of which takes 12.5 min.

i.e. he will take a total of 12.5x minutes in painting 'x' chairs.

Also total time spent on painting furniture each day will be equal to time spent on painting a desk and all of the chairs.

Hence,

30.5+12.5x<120 (since the total time he spends on painting is less than 120 mins.)

⇒ 12.5 x<120-30.5

⇒ 12.5 x<89.5

⇒ x<7.16 ( on dividing both side of the inequality with 12.5)

Hence, a carpenter can paint a maximum of 7 chairs.

Nadya [2.5K]3 years ago

6 0

Most
assume 120 mins

30.5 spent
120=30.5=89.5 left

time/timeperdesk=number of desks
89.5/12.5=7.16

less
7 desks

A

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$y=8 \cdot (\frac{5}{4})^x$

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or

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Step-by-step explanation:

We are going to see if the exponential curve is of the form:

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If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

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So $a=8$ .

So our function so far looks like this:

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Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

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This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

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$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

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So we are good. We have found an equation satisfying all 3 points given.

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