Tutors, sign in to answer this question.

The exercise is to match up the words with mathematical functions, and solve algebraically:

Let X = total money

"Jo spent 40": X -40

"and spent half of her remaining": -(1/2)(X-40)

"then spent 29.45": -29.45

(X - 40) -(1/2)(X-40) -29.45 = 17.75 "has 17.75 left"

X - 40 - (1/2)X + 20 - 29.45 = 17.75

(1/2)X -20 - 29.45 = 17.75

X = 2*(20+ 29.45 + 17.75)

X = $134.40

Hi Brent,

Let's look and the second sentence first:

She spent 29.45 and had 17.75 left over. That means she had 29.45 + 17.75 after her first purchase.

If she spent half of her remaining then this is the other half. So, add the two halves together and don't forget the $40.

let x= how much money she had to begin with

x-40-(1/2)(x-40)-29.45=17.75

x-40-(1/2)x+20-29.45=17.75

(1/2)x-49.45=17.75

(1/2)x=17.75+49.45

(1/2)x=67.20

x=$ 134.40

check: 134.40-40=94.40

94.40-(1/2)(94.40)=94.40-47.20=47.20

47.20-29.45=$ 17.75

Hi Brent;

Let's simplify this...

After she spent the $40 and half which remained, she had

29.45+17.75=47.20

So...

x=original amount

x-[40.00 + ((40.00-x)/2)]=47.20

x-40.00+(40.00/2)-x/2=47.20

(x/2)-20.00=47.20

Let's isolate x by adding 20.00 to both sides...

20.00+(x/2)-20.00=47.20+20.00

x/2=67.20

Let's multiply both sides by 2...

2(x/2)=67.20(2)

x=134.40

Let's check our work...

134.40-40.00=94.40

She then spent half...

94.40/2=47.20

She then spent 29.45...

47.20-29.45=17.75

Please note, that throughout the equations, I indicated all numbers as 00.00. In other words, whether or not there were any cents, I indicated such. It is important to be consistent.

Let's write the equation

x - 40

x − 40 − -------- − 29.45 = 17.75

2

x − 40

x − ----------- = 17.75 + 40 +29.45

2

x − 40

x − ---------- = 87.20

2

2x − (x − 40) = 2 × 87.20

2x − x + 40 = 174.40

x = 174.40 − 40

~~~~~~~~~

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.