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# Jo spent 40\$ adn half of her remaing money. She then spent 29.45 and has 17.75 left. How much did she have?

Jo spent 40\$ adn half of her remaing money. She then spent 29.45 and has 17.75 left. How much did she have?

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;
Jo spent 40\$ and half of her remaining money. She then spent 29.45 and has 17.75 left. How much did she have?

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.
So,

2. (x - 40) dollars is remain, after spending of \$40

3. Then she spent half of remain, that is
x - 40
-------
2

4. Then she spent \$29.45

5. She has \$17.75 left.

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

x = 134.40 dollars.

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