Robby's Scribe

Today in class, we got this algebra work sheet. So, I'll do some of the questions on the number-answer sheet, not geometry side.

Question 1:

The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.

Ok, so, to answer this question, we have to find out which is the variable and have it equal 50. It also says "sum", so there is going to be addition in this question.
To find the variable, you have to read the sentence and find out what part of the question isn't told. But first, write the simple-sentence answer, which is just the answer in a sentence. You write this out first, then come back to it once u find the numbers.

10 40
The numbers are ____ and ____. (You can also write this at the end of the equation, which is what I'm going to do just to make it make more sense.)

"The second of two numbers"
This means that, in the equation, the second number will NOT be the variable, because if u read on..."is 4 times the first". This means it will be 4x, not just x, which is what we need.
So the first number will be x.
Remember, you have to have the "Let X = blahblah" somewhere in that equation, or u lose marks.

Moving on, 4x would be on the right side of the + sign, because it is the second number. The first number is x.
So the equation would look like this:
Let x = First number
x + 4x = 50 (what we have so far)
5x = 50 (combined like terms)
-- ---
5 5
x = 10
The answer to this question would be 10, 40.

SUBSTITUTE TO CHECK (this is to make sure you have the right answer)
x + 4x = 50 (must write formula)
10 + 4(10) = 50
10 + 40 = 50
50 = 50

x = 10
4x = 40 (this is very important too, before you write your answer into the sentence, you have to write out what the variable and term stand for in numbers, like above. Now you see why its easier to write the sentence at the bottom)

If the answer on the left side equals the right side (50 = 50), that means the number works.

Question 2:

(I will now be writing all the answers out with some info in brackets, if you don't get it, go back to Question 1: and read on how to get it.)

The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers.

"Larger of two numbers is 12 more than smaller"

The two other numbers would equal x, because nothing is told about them.

Let x = Smaller Number 1, Smaller number 2.

x + 12 + x + x = 84
3x + 12 = 84 (combined like terms)
-12 -12
3x = 72
-- ---
3 3
x = 24

Substitute to Check:

x + 12 + x + x = 84
3(24) + 12= 84
72 + 12 = 84
84 = 84

x+12 = 36
x = 24
x = 24

36 24 24
The numbers are ____, ____, and ____.

The answer would be 36, 48 [because 36 is 24 + 12 and 48 is 24 + 24 (2 x 24)]

Question 4:

The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.


"second of two numbers"
So the second number would be the term (number with the x or a or whatever letter next to it)
and the first number would be the variable.

Let x = First Number

"5 more than twice the first"
2x + 5
"sum is 80"
= 80
Now put it al together...

x + 2x + 5 = 80
3x + 5 = 80
- 5 -5
3x = 75
-- ---
3 3

x = 25

Substitute to Check:

x + 2x + 5 = 80
3(25) + 5 = 80
75 + 5 = 80
80 = 80

2x+5 = 55
x = 25
25 55
The numbers are _____, and _____.
25, 55.

Question 6:

Find two numbers whose sum is 92, if the first is 4 more than 7 times the second. Find the First number.

"Two numbers whose sum is 92, if the first is 4 more than 7 times the second"
so the second number is x, because it doesn't mention anything about it.

Let x = Second Number

(7x + 4) + x = 92 (brackets there to make it look simpler)
8x + 4 = 92 (combined like terms)
- 4 -4
8x = 88
-- --
8 8
x = 11

Substitute to check:

(7x + 4) + x = 92
8(11) + 4 = 92
88 + 4 = 92
92 = 92

x = 11
7x + 4 = 81

The first number is 11.

Question 8:

Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet.

"if the necklace costs 3 times as much as the bracelet"

This means the bracelet is x.
Let x = bracelet

3x = Necklace

3x + x = 192
4x = 192
-- ----
4 4
x = $48 ($48.00)

Substitute to check:

3x + x = 192
4(48) = 192
192 = 192

(now to find the price of a necklace and bracelet separately)

3x = 3(48)
= 144
x = 48

$144.00
+$48.00
--------
$192.00

The price of a bracelet is $48.00 and the necklace is $144.00.