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Karo-lina-s [1.5K]
3 years ago
11

If 15% of the customer's total is $22.05, then the customer's total is _______."

Mathematics
2 answers:
vesna_86 [32]3 years ago
7 0

Answer:

$147

Step-by-step explanation:

15% over 100 is .15

So you get .15x= 22.05

Get x by itself by dividing .15 by .15

whatever you do to one side you have to do to the other so divide 22.05 by .15 and you get $147

avanturin [10]3 years ago
3 0

let's say is "x", so "x" is then 100% of the whole bill.

we know 15% is 22.05, what is "x"?

\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 22.05&15\\ x&100 \end{array}\implies \cfrac{22.05}{x}=\cfrac{15}{100}\implies 2205=15x \\\\\\ \cfrac{2205}{15}=x\implies 147=x

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The first three terms of an arithmetic progression are m,12 and n . Find the value of m+n​
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<h3>Answer:  24</h3>

===========================================

Explanation:

There are a few approaches. Here's one way to solve.

Let d be the common difference between the terms.

We add d to each term of this arithmetic sequence to get the next term.

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It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.

-----------------

A more concrete example:

Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.

Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.

If d = 10, then the third term must be n = 12+d = 12+10 = 22

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-----------------

I'll do another example:

m = 5

d = 12-m = 12-5 = 7

n = 12+d = 7 = 19

m+n = 5+19 = 24

Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.

-----------------

An alternative way to get the answer:

Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.

The midpoint of m and n is (m+n)/2

Set this equal to 12 and isolate the "m+n"

(firstTerm+thirdTerm)/2 = second term

(m+n)/2 = 12

m+n = 2*12

m+n = 24

So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.

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