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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

~~~~~~~~~

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