An office manager will spend a total of $37 comma 500 on computers at $1500 each and printers at $1200 each. Write the number of computers purchased as a function of the number of printers purchased. Find and interpret the slope.

Question

Mathematics

Khalil Parsons

Today, 16:16

An office manager will spend a total of $37 comma 500 on computers at $1500 each and printers at $1200 each. Write the number of computers purchased as a function of the number of printers purchased. Find and interpret the slope.

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Answers (2)

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Humberto Sexton · Answer 1

37500 = 1500 X + 1200 Y

Step-by-step explanation:

Total $37500 is spend on both computer and printers and 1500 at each computer and 1200 at each printer.

Where X=number of Computer and Y = number of printers so we have

equation is equal to 37500 = 1500X + 1200Y

Function: 1500X = 1200 Y - 37500

X = 1200 Y - 37500

1500 1500

X = 3/4 Y - 25.

Slope (m) = ?

we have Y = mx + b

by comparison with equation

X = 3/4 y + (-b)

then m=3/4=.75

if each printer is purchased we predict that office manger cost 24.5 each increase in computer

Ross Moss · Answer 2

the slope is - (4/5) for an increasing number of printers bought the number of the computers bought will decrease.

Step-by-step explanation:

firstly we are told that we must write the number of computers purchased as a function of the number of printers purchased therefore this tells us that we must let X be the number of printers and let Y be the number of Computers purchased.

on the statement we are told the costs per computer of $1500 and we are also told the cost per printer which is $1200 each then they further tell us that we have a total of $37500 to spend so if we put this in one equation it will be:

$1500Y + $1200X = $37500 because we let the number of each computers bought be Y and each of the number of printers bought be X.

now we will solve for to make Y the subject of the formula as we are told above that the number of computers (Y) purchased is a function of the number of printers (X) bought.

$1500Y = $37500 - $1200X, we transpose the dependent variable then we divide the whole equation by $1500 to make Y the subject of the formula.

Y = 25 - (4/5) X then we rearrange to the format Y = mX + c

Y = - (4/5) X + 25

then we get a negative slope which tells us that for an increasing number of printers bought the number of the computers bought will decrease.