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

a) Abby's expression

`2x-(20* 2x)/(100)`

Renato's expression,

`(x)/(5)* 8`

b) Both methods will give the same answer.

Explanation:

a) Let x be the number of miles,

∵ Double of x = 2x,

20% of 2x =
`(20* 2x)/(100)`

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

=
`2x-(20* 2x)/(100)`

Which is Abby's expression,

Now, Renato's expression of kilometers in x miles =
`(x)/(5)* 8`

`=(8x)/(5)`

b)
`\because 2x-(20* 2x)/(100) = (200x-40x)/(100)=(160x)/(100)=(8x)/(5)`

Hence, two methods will give the same answer.

Answer 2

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