Algebra

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Can someone check my work for the following? I am supposed to use the five-step method to solve & check, but I don't know what that is. Anyway

1. One-third of a number is 5 less than half of the same number. What is the number?

My answer:
1/3x = 1/2x - 5
6(1/3x) = 6(1/2x) - 6( 5)
2x =3x - 30
2x - 2x = 3x - 30 - 2x
0 = x - 30
0 + 30 = x - 30 + 30
30 = x

x = 30

And to check:
1/3x = 1/2x - 5
1/3(30) = 1/2(30) - 5
30 / 3 = 30 / 2 - 5
10 = 15 - 5
10 = 10

2. The sum of a number and its reciprocal is 10/3. What is the number?

My Ans:
x+1/x= 10/3
(x^2+1)/x= 10/3
3 ( x^2+1)= 10 x
3x^2+3= 10x
3x^2-10x+3= 0
( 3x-1) ( x-3) = 0
3x-1= 0
x= 1/3
x-3= 0
x= 3

Check:
x+1/x= 10/3
3 + 1/3= 10/3
(9+1)/3= 10/3
10/3= 10/3

3. An investment of $1500 paid interest of $45 during a certain period. How much interest would an investment of $2000 invested at the same rate for the same length of time pay?

My Ans:
45/1,500=X/2,000
1,500X=45*2,000
1,500X=90,000
X=90,000/1,500
X=$60

Check:
45/1,500=60/2,000
90,000=90,000


4. In baseball a player's batting average is the ratio of hits to the number of times he or she has batted. Thus, if the player has an average of .3000, it means he or she got 300 hits in 1000 at bats. In order to have an average of .300, how many hits would the batter have to get in 400 times at bat?

My Ans:
batting average=(hits)/(times batted)
your batting average =.300
times batted=400
hits=x


.300 = x/400
(400).(.300)= 400x/400
120 = x

Check:
.300 = 120/400
.300 = 300

Thanks in advance everyone.

  • Algebra -

    1, 2, and 4 are right. I'm not sure about 3.

  • Algebra -

    #3 is correct
    another way to do #3 is to simply set up a ratio

    x/2000 = 45/1500
    x = 45(2000)/1500
    = 60

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