Question

1. The sum of a number and 2 is 6 less than twice that number.

2. A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.

4. Six times a number is less than 72. What numbers satisfy this condition?

5. A number increased by 10 is greater than 50. What numbers satisfy this condition?

I am confused as to how to convert them into equations. These are not test questions I promise. Can someone please help clear the darkness a little?

Answer 1

In many of these it is important to see what "verbiage" can be ignored and to key in on the critical phrases.
e.g. #2
- "rectangular" is important since we need the perimeter
- "a width that is 8 feet less than twice the length"
The reference was "the length", so let the length be x
I see "twice the length" ----> 2x
I see "8 feet <b>less than</b> 2x -----> 2x - 8
I know the perimeter is : twice the length + twice the width
= 2(x) + 2(2x-8)
But we are told that equals 20 , so
2x + 2(2x-8) = 20
Now just solve that

let's try another:
#5 A number increased by 10 is greater than 50.
" a number" ---- x
"increased by 10" ---- +10
"is greater than" ----- >
x + 10 > 50
etc

Answer 2

Simplification

1.

x + 2 = 2 x - 6,

2.

W = 2 L - 8

P = 2 ( L + W ) = 2 ( L + 2 L - 8 ) = 2 ( 3 L - 8 ) = 6 L - 16 = 20

6 L -16 = 20

4.

6 x < 72

5.

x + 10 > 50

Try to solve this equations.

Answer 3

Looking at #1,
-- The sum of a number and 2 is 6 less than twice that number --

Some students find this type of problem confusing. Do I add or subtract that 6?
I know there is a < somewhere.

I suggested that they rephrase the problem:
"The sum of a number and 2 is less than twice that number by 6 "
x + 2 < 2x by 6
so right now the 2x is the bigger part by 6
so if we subtract 6 from the right side, they would be equal, so
x + 2 = 2x - 6
x = 8

check:
the sum of the number and 2 : 8 + 2 = 10
twice the number: 16
is 10 less than 16 by 6 ? YES

Answer 4

I am a 3 - digit number. I have 6 in the ones place. I am greater than 127 but less than 142. What am I?