If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week? (1) Last week Bob was paid total of $480 for the items that he produced that week. (2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

Question

Katrina Rush

Mathematics

8 October, 15:42

If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week? (1) Last week Bob was paid total of $480 for the items that he produced that week. (2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

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Dallas Martin · Answer 1

How many items did Bob produce last week? 32 items.

Step-by-step explanation:

(1) Last week Bob was paid total of $480 for the items that he produced that week.

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

a) Let's start with the simplest case: he produced 36 or less items this week.

In this case he produced less than 36 items last week too.

So he was paid the same amount of dollar per item.

Using (1) and (2) assumptions we have:

$480+2X=$510

⇒2X=$510-$480

⇒2X=$30

⇒2X=$30/2

⇒X=$15

He was paid $15 per item.

Last week he was paid $480.

480/15 = 32 items.

This week he was paid $510.

510/15=34 items.

The other cases has no solutions.