Answer:
Step-by-step explanation:
What this question is asking of you is what is the greatest common divisor of 12 and 15. Or, what is the biggest number that divides both 12 and 15.
in order to find this we have to split each number into it's prime components.
for 12 they are 2,2 and 3 (
2
⋅
2
⋅
3
=
12
)
and for 15 they are 3 and 5 (
3
⋅
5
=
15
)
Out of those two groups (2,2,3) and (3,5) the only thing in common is 3, so 3 is the greatest common divisor. That tells us that the greatest number of groups that can exist and have the same number of girls and the same number of boys for each group is 3.
Now to find out how many girls and boys there are going to be in each group we divide the totals by 3, so:
12
3
=
4
girls per group, and
15
3
=
5
boys per group.
(just as a thought exercise, if there were 16 boys, the divisors would have been (2,2,3) and (2,2,2,2), leaving us with 4 groups [
2
⋅
2
] of 3 girls [12/4] and 4 boys [16/4] )
Answer:
1 
more cups of flour
Step-by-step explanation:
Answer:a = - 2
b = - 3
c = 3
Step-by-step explanation:
a + 5b - c = - 20 - - - - - - - - - 1
4a - 5b + 4c = 19 - - - - - - - - - 2
-a - 5b - 5c = 2 - - - - - - - - - - - 3
Adding equation 1 and equation 2, it becomes
- 6c = - 18
c = - 18/ - 6 = 3
Multiplying equation 2 by 1 and equation 3 by 4, it becomes
4a - 5b + 4c = 19
-4a - 20b - 20c = 8
Adding both equations, it becomes
- 25b - 16c = 27
- 25b = 27 + 16c = 27 + 16 × 3
- 25b = 75
b = 75/- 25 = - 3
Substituting b = - 3 and c = 3 into equation 1, it becomes
a + 5 × - 3 - 3 = - 20
a - 15 - 3 = - 20
a - 18 = - 20
a = - 20 + 18 = - 2
Answer:
3. A=B=70°; C=D=110°
4. A=90°; C=48°
Step-by-step explanation:
Same-side angles of a trapezoid add to 180°.
___
3. (2x) +(x+15) = 180
3x + 15 = 180 . . . . simplify
x +5 = 60 . . . . . . . divide by 3
x = 55
A=B=(x+15)° = (55+15)° = 70°
C=D=2x° = 2·55° = 110°
__
4. You are given the values of one of the angles on each side, so the other can be found by subtraction:
A=180°-D = 90°
C = 180° -132° = 48°
Answer:
Karen had 45 m and m's candy.
Step-by-step explanation:
Let the number of m and m's candy be 'x'.
Now given:
Karen gave an equal amount of m and m's to herself and four friends.
So we can say that;
Number of people m and m's candy distributed equally = 5
Also Given:
Each person receives m and m's equivalent to the largest one digit number.
Now we know that;
Largest one digit number is 9.
So we can say that;
Each person receives m and m's = 9
We need to find number of m and m's Karen have.
Solution:
So we can say that;
Total number of m and m's Karen have is equal to Number of people m and m's candy distributed equally multiplied by number of m and m's can each person receives.
framing in equation form we get;
Total number of m and m's Karen had = 
Hence Karen had 45 m and m's candy.
