Which simpler problems could be calculated to solve this problem?

Richard bought 3 bottles of water for $1.50 each and a tray of sandwiches for $20. He gave the cashier an 8% tip. How much change did Richard get back from $30?

A.
Calculate the total cost of the 4 items. Calculate the tip. Add the tip to the price of each item. Calculate the change.

B.
Calculate the total cost of the 4 items. Calculate the tip. Add the tip to the total cost of the items. Calculate the change.

C.
Calculate the tip of each item. Calculate the total of the tips. Add the tip to the cost of each item. Calculate the total cost. Calculate the change.

D.
Calculate the tip. Calculate the total cost of 4 items. Add the tip to the cost of each item. Calculate the change.

Option B

Step-by-step explanation:

We first need to calculate the total cost of all the four items then calculate the tip of the total cost. After this we add the tip to the cost of items and calculate change as follows.

Total cost of items

Cost of bottles =3*1.5=$4.5

Cost of sandwitches= $20

Total cost= 20+4.5=$24.5

Tip=0.08*24.5=$1.96

Total=24.5+1.96=26.46

Change= 30-26.46=$3.54

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!

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5