Solving

Level 1

100

0.4x-0.7=0.3x

7

200

2x-0.6=0.5

11/20

300

2x-4=5x-13

3

400

2x-1=4+x

5

500

0.05x-0.02=0.28-0.01x

5

100000

5x-2=6+x

2

Level 2

100

2/3-3/2x=-1/3x-4

4

200

1/5x+2/3-2=x-2/5

-7/6

300

0.7x+0.5=0.2x+1

1

400

6/4x+3/8=2

13/12

500

0.25+0.5x=4

15/2

100000

0.25x+x=-3+0.5x

-4

Level 3

100

3x-6/3=3/4x+9/4

17/4

200

x+8/3=1/2+1/4x

-26/9

300

-7.5-8.99x=2.1x+3.55

-1

400

7/4x-3=2+9/2x

-20/11

500

0.25x+0.4x=0.5x-0.45

-3

100000

1/3-2/9x=15+x

-12

Opposites

100

yes

no

200

hi

bye

300

hot

cold

400

smart

noah

500

high

low

100000

thin

thicc

Level 5000

100

1+1

2

200

2+2

4

300

3+3

6

400

4+4

8

500

5+5

10

100000

C=59(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
2. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
3. A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

ANSWER EXPLANATION: Think of the equation as an equation for a line

y=mx+b

where in this case

C=

59(F−32)

or

C=

59F−59(32)

You can see the slope of the graph is 

59, which means that for an increase of 1 degree Fahrenheit, the increase is 59 of 1 degree Celsius.

C=

59(F)

C=

59(1)=59

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 

95 degrees Fahrenheit.

C=

59(F)

1=

59(F)

(F)=

95

Since 

95 = 1.8, statement II is true.

The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 

59 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

C=

59(F)

C=

59(59)

C=

2581(whichis≠1)

An increase of 

59 degree Fahrenheit leads to an increase of 2581, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.