Last week Rachel walked 2 and 3/5 miles per day on each of the 7 days. During the same week, she also jogged 5 and 3/4 miles per day on 4 days. How many total miles did Rachel walk and jog last week?

41.2 miles was the total number of miles Rachel power walked and jogged last week

Step-by-step explanation:

Unit rate are defined as the rate are expressed as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.

As per the given statement: Last week Rachel power walked 2 3/5 miles per day on each of the 7 days.

⇒

Total number of miles she walked in 7 days =

= miles

Also, it is given that during the same week, she also jogged 5 3/4 miles per day on 4 days.

⇒

Total number of miles she jogged in 4 days =

= miles

Total number of miles Rachel power walked and jogged last week = 18.2 +23 = 41.2 miles

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.