three questions guess and check?

Question

1. A's score on math was 80% B's score on science was 80% also. B had 12 more correct answers than A. Together their correct answers totaled 52. How many questions were on each test? 2. The numerator and denominator of a certain fraction are in the ratio 4:7 The denominator of the fraction is 15 more than the numerator.What is the fraction? 3. At an end of season sale. Lu bought a coat and a dress on sale for 50% off the original price of each. She spent a total of $150 for both items. The original price of the coat was $20 more than the original price of the dress. What was the original price of each? Thank you all who are smarter than me and your explainations to be able to explain it to my 6th grader!

Answer 1

1)
B = A + 12
A + B = 52
A + (A + 12) = 52
2 A + 12 = 52
2 A = 40
A = 20 correct
B = A + 12 = 32 correct

**For B to have 80% then 80% of what is 32?
8/10 x = 32
solve x = 40 Thus there are 40 questions on B's test

**For A his score is 80% similar approach
8/10 x = 20
x = 25 Thus there are 25 questions on A's test

2) 4x/7x is the fraction in the question
4x + 15 = 7x
solve... 3x = 15, x = 5 thus the fraction is 20/35

3) .5 (Coat + Dress) = 150
Coat = Dress + 20
.5 ( Dress + 20 + Dress) = 150
.5 (2 Dress + 20) = 150
Dress + 10 = 150
Dress = 140
Coat = 160

Answer 2

1. Since A and B both had 80% of the correct questions, then when you add them together and get 52, 52 is 80% of the total number. 52/80 will give you 1% and multiply that by 100 and it will give you 100% of the questions. The total number of questions would be 65.

B had 12 more correct answers than A. The correct answers are 80% of all the answers. So if 12 is is 80% Then what is 100%?
12/80*100= 15 So B had 15 more questions than A

If you gave A 7 1/2 question and took 7 1/2 questions from B, they would have the same. 65/2= 32 1/2 questions each if they had the same.
32 1/2 - 7 1/2= 25
32 1/2 +7 1/2= 40

Your kid is takeing some pretty hefty math for a 6th grade.

4/7 = x/(x+15)

4 (x+15) = 7x
4x + 60 = 7x
60 = 3x
60/3 = x
20 = x

20/35 was the fraction



50% off and paid $150 total. Would have paid $300

The original price of the coat was $20 more than the dress
Add $10 to the dress and take away $10 from the coat and it would be the same...

$150 would be the same for each item

The dress cost $140 and the coat was $160

Answer 3

Ok.
1.- 52-12=40/2=20 So A had 20 correct answers and B 32 correct answers. 20 and 32 are only the 80% of each test, therefore A= 20*100/80=25, and B. 32*100/80=40.
A test was of 25 questions and B test was of 40.

2. Numerator 20, denominator 35. or 20/35. You simply multipy this fraction by 1, 2, 3, etc, until the numbers match.

3. The difference in the original price shorted to 10 with the discount. you quit such amount from 150 and divide on 2. 150-10=140/2=70.
So you have a coat that costed you 80 but that the original price was 160.
And you have a dress that costed 70, but the original price was 140.

Answer 4

For guess and check, you must first choose answers that fit one of the conditions of the problem and then see if the fit the other one also. For example, on problem 1, 80% is 4/5 as a fraction so pick a fraction equal to 4/5, say 8/10. Then the other person would have 20 right, so you need 20/25 to be able to reduce to 4/5. However, 8+20 is only 28 questions and you need 52. So make a second starting guess, say 16/20. Then B needs 28 right, and 16+28 is 44, not 52. So guess again, start with 20/25. Then B needs 32 and 20+32=52 so that's it. In New York State, you need at least 2 wrong guesses to get full credit when using guess and check (don't ask me why, that's just how the state ed dept wants it).

Answer 5

Ok...Wow...I do not recall 6th grade problems as difficult in my day. That said, I will lend you a hand...but you must promise to work the problems yourself with your kid.

1) A = 0.80 = (A correct)/Total Questions for A
B = 0.80 = (B correct)/Total Questions for B

B correct = A correct + 12 (1)

Acorrect + B correct = 52 (2)

How many questions on each test?

Solving for B correct by combining equations (1) and (2)

2B correct = 64
Bcorrect = 64/2 or 32 correct answers
Acorrect = Bcorrect - 12
Acorrect = 20 correct anwers

Recall that A got an 80% score = Acorrect/Total questions

Total Questions for A= Acorrect/0.80 = 20/0.80 = 25 questions for A
Total Questions for B = Bcorrect/0.80 = 32/0.80 = 40 questions for B

Problem 2.

Num/Den has a ratio of 4:7

Denominator=Numerator+15

What is the fraction?

Using the ratio expression, we can determine the fraction.

4/7 = Numerator/(Numerator+15)
4*(Numerator+15) = 7Numerator ..........(Cross multiplying)

4Numerator + 60 = 7 Numerator

4 Numerator -4Numerator + 60 = 7Numerator-4Numerator

60 = 3 Numerator

Solving for Numerator,

Numerator = 60/3 or 20

Recall Denominator = Numerator + 15 = 20+15=35

So, finally, fraction is given as 20/35 (or a ratio of 4/7)

3) 0.50(Original_Coat +Original_Dress) = 150 ..............(1)
Original_Coat= Original_Dress+20 ....................(2)

What is the original Price of each?

Multiply Equation 1 by 2

Original_Coat + Original_Dress = 300

You know Original_Coat = Original_Dress+20

Substituting in above equation:

Original_Dress+20+Original_Dress=300

2Original_Dress= 300-20=280

Original_Dress= 280/2 = $140

Original_Coat=Original_Dress+20 = $140+$20 = $160

Good Luck!

Answer 6

Duh, never learned guess & check, except for Transcendentals. Algebra is SO much easier!
80*B/100 -80*A/100 = 12
80*B/100+80*A/100 = 52
160*B/100 = 64
B = 6400/160 = 40
80*40/100 + 80A/100 = 52
3200 + 80A = 4200
80A = 1000
A = 125

4/7 = n/(n+15)
4n+60 = 7n
3n = 60
n = 20

C/2 + D/2 = $150
C - D = $20
C + D = $300

2C = $320
C = $160
D = $140