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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?

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5 Answers

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,
1. Jo had "x" dollars.

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.

~~~~~~~~~

Let's check the answer:
134.40 - 40 = 94.40
94.40 ÷ 2 = 47.20
47.20 - 29.45 = 17.75

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