8. Abby, Ingrid, and John are sharing a bag of candy in the extended ratio 2:3:4. If there are sixty three candies in the bag, then how many will Ingrid get?
A. 7
B. 14***
C. 21
D. 28
9. Which of the following are equivalent to the ratio 3ab:27ab? Select all that apply.
A. 1:9
B. 9a:81a***
C. a:b
D. a:3b***
E. 2:18***
F. 3b:27a
10. Which of the following are equal to the ratio (2 x-6) : (6x-4)?
A. -2 : 1
B. x - 3: 3x - 2***
C. 3x : x
D. (4x-12) : (12x - 8)
E. x - 1 : x - 2***
Please check and help :( I think I'm wrong on at least half but I have no idea
The entire Practice test- in order 1-10
B
C
D
C
D
A
C
C
A-B-E
B-D
Thanks Mr.RightGuys
@Mr.RightGuy 100% thanks
#8
2x+3x+4x = 63
x = 7
So, the actual quantities are
14:21:28
#9
3ab/27ab = 1/9
So, A,B,E are the equivalent ratios. D doesn't get rid of the a,b stuff.
Odd how you could get B and E right, but miss A and pick D...
#10
B and D only
8.
A = Abby's part
I = Ingrid's part
J = John's part
There are sixty three candies in the bag.
This mean:
A + I + J = 63
A / I / J = 2 / 3 / 4
This mean :
A / I = 2 / 3
I / J = 3 / 4
so:
A / I = 2 / 3 Multiply both sides by I
A = 2 I / 3
A = ( 2 / 3 ) I
I / J = 3 / 4 Multiply both sides by 4
4 I / J = 3 Multiply both sides by J
4 I = 3 J Divide both sides by 3
4 I / 3 = J
J = 4 I / 3
J = ( 4 / 3 ) I
Replace this value in equation:
A + I + J = 63
( 2 / 3 ) I + I + ( 4 / 3 ) I = 63
( 2 / 3 ) I + ( 3 / 3 ) I + ( 4 / 3 ) I = 63
( 9 / 3 ) I = 63
3 I = 63 Divide both sides by 3
I = 63 / 3 = 21
9.
3 a b : 27 a b = 3 a b : ( 9 * 3 a b ) = ( 3 a b : 3 a b ) * 1 : 9 = 1 * 1 : 9 = 1 : 9
10.
( 2 x - 6 ) : ( 6 x - 4 ) =
2 * ( x - 3 ) : [ 2 * ( 3 x - 2 ) ] =
(2 : 2 ) ( x - 3 ) : ( 3 x - 2 ) =
1 * ( x - 3 ) : ( 3 x - 2 ) =
( x - 3 ) : ( 3 x - 2 )
Thank you guys!
Remark :
1 * ( x - 3 ) : ( 3 x - 2 ) =
( x - 3 ) : ( 3 x - 2 )
4 / 4 = 1 so :
( 4 / 4 ) * ( x - 3 ) : ( 3 x - 2 )
4 * ( x - 3 ) : [ 4 * ( 3 x - 2 ) ] =
( 4 x - 12 ) : ( 12 x - 8 )
Question 10
Answers B and D
what grade is this for
Let's break down each question and explain how to get the answer:
8. Abby, Ingrid, and John are sharing a bag of candy in the extended ratio 2:3:4. If there are sixty-three candies in the bag, then how many will Ingrid get?
To find out how many candies Ingrid will get, we need to determine her share based on the extended ratio. First, we need to calculate the sum of the parts in the ratio: 2 + 3 + 4 = 9.
Next, we divide the total number of candies by the sum of the parts: 63 / 9 = 7.
Since Ingrid's share is represented by the 3 in the ratio, she will get 7 candies.
Therefore, the answer is B. 14.
9. Which of the following are equivalent to the ratio 3ab:27ab? Select all that apply.
To find ratios that are equivalent to 3ab:27ab, we can simplify the ratio:
3ab:27ab can be simplified by dividing both sides by the common factor of 3ab:
3ab ÷ 3ab = 1
27ab ÷ 3ab = 9
Simplified, the ratio becomes 1:9.
The equivalent ratios can be determined by multiplying or dividing both sides of the simplified ratio by the same factor. Let's check all the options:
A. 1:9 - The original ratio, which is equivalent. ✓
B. 9a:81a - By multiplying both sides of the simplified ratio by 9, we get 9:81, which simplifies to 1:9. ✓
C. a:b - Not equivalent to the original ratio.
D. a:3b - By dividing both sides of the simplified ratio by 3, we get 1:3. Not equivalent to the original ratio.
E. 2:18 - By multiplying both sides of the simplified ratio by 2, we get 2:18, which simplifies to 1:9. ✓
F. 3b:27a - Not equivalent to the original ratio.
The equivalent ratios are A. 1:9, B. 9a:81a, and E. 2:18.
10. Which of the following are equal to the ratio (2x-6) : (6x-4)?
To find ratios that are equal to (2x-6) : (6x-4), we can't simplify the ratio any further since there are no common factors between the two terms.
Let's check each option to see if they are equal:
A. -2:1 - Not equal to the original ratio.
B. x-3:3x-2 - This is equivalent to the original ratio since the terms can't be simplified further. ✓
C. 3x:x - Not equal to the original ratio.
D. (4x-12):(12x-8) - Not equal to the original ratio.
E. x-1:x-2 - Not equal to the original ratio.
The only option that is equal to the given ratio is B. x-3:3x-2.
I hope this helps! Let me know if you have any further questions.