At the beginning of the first day, a company has 64 shipping crates on backorder. by the end of each day, customers order 18 more shipping crates. if the company employees work overtime and make 28 shipping crates every day, how many crates will be on backorder at the beginning of the fifth day? a. 14 b. 16 c. 34 d. 24

The correct answer option is A. 14.

Step-by-step explanation:

Assume x to be the number of days.

On the first day, the company begins with 64 orders and gain 18 more orders per day which makes it 18x and we get:

64 + 18x

Moreover 28 crates per day are made, which decreases the number of crates that are needed per day by 28 which makes it -28x, and we get:

64 + 18x - 28x

Combining like terms, we get

64 - 10x

For day 5, we substitute the value of x with 5:

64 - 10(5) = 64 - 50 = 14

Therefore, 14 crates will be on back-order at the beginning of the fifth day.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

range is infinite on both x and y axis positive and negative

step-by-step explanation: