Question

The students in Mr. Sanchez's class are converting distances measured in miles to kilometers. To estimate the number of kilometers, Abby takes the number of miles, doubles it, then subtracts 20% of the result. Renato first divides the number of miles by 5, then multiplies the result by 8.
a) Write an algebraic expression for each method


b) Use your answer to part (a) to decide if the two methods give the same answer.

Answer 1

Let 
x-----------> the distances measured in miles

 Abby method 
1)2x
2)2x-20%------> 2x-0.4x
algebraic expression-----> [2x-0.4x]---------> 1.6x

 Renato method 
1)x/5
2)(x/5)*8-------> 8x/5
algebraic expression----->[8x/5]---------------> 1.6x

Part B)
[2x-0.4x]=[8x/5]---------> 1.6x=8x/5--------> 5*(1.6x)=8x-------> 8x=8x
therefore
the two methods give the same answer
the answer is 1.6x

Answer 2

Answer:

a) Abby's expression

$2x-\frac{20\times 2x}{100}$

Renato's expression,

$\frac{x}{5}\times 8$

b) Both methods will give the same answer.

Step-by-step explanation:

a) Let x be the number of miles,

∵ Double of x = 2x,

20% of 2x = $\frac{20\times 2x}{100}$

Thus, number of kilometers in x miles = 2x - 20% of 2x

= $2x-\frac{20\times 2x}{100}$

Which is Abby's expression,

Now, Renato's expression of kilometers in x miles = $\frac{x}{5}\times 8$

$=\frac{8x}{5}$

b) $\because 2x-\frac{20\times 2x}{100} = \frac{200x-40x}{100}=\frac{160x}{100}=\frac{8x}{5}$

Hence, two methods will give the same answer.