How do I solve this I keep getting this wrong?

Question

A local bank has a debit card that gives a $3 reward each month when you use your card for $50 or more in a purchase.

write an equation relating rewards earned ,y, to total monthly purchases ,x. Give the domain of this function.

Answer 1

This is not going to work....

The bank gives $3 reward each month when the card is used

for a SINGLE PURCHASE of $50 or more.

You cannot base this function on the total of the purchases...

For example, I can make the following purchases:

$20

$25

$20

$25

$20

$30

$25

$20

$40

$20

$25

$30

The total of these purchases is $300. But I do not deserve a

single reward for these purchases because ALL of them are

less than $50.

If you want it to be based on the total of the purchases, then you

MUST REWRITE the rule. It should say "A local bank has a debit card

that gives $3 reward each month FOR EVERY $50 WORTH OF PURCHASES"

In that case, the function is:

y = INT(x / 50) * 3 where x is the total of the purchases and the INT() function

returns the integer portion of the division and throws away the fraction.

EX. If the total of the purchases is X=$275, then y = INT(275/50) * 3

= INT( 5.5) * 3

= 5 * 3

= 15

Otherwise, you have to REDEFINE x to be a SINGLE purchase. In that case, the

function is

y = {

3 if x>=50,

0 otherwise

}

I'm sorry it is so complicated.

I hope you understand the difference.