Mrs. gomez is a mother to 2 boys. the number of children she has is three times the number of boys she has. her children are planning to buy her a bouquet of flowers. what is the biggest bouquet they can buy in which the ratio of pink flowers to blue flowers matches the ratio of girls to boys if the florist has 9 blue carnations and 12 pink carnations left?
a bouquet of 12 flowers, 4 pink and 8 blue
a bouquet of 14 flowers, 8 pink and 6 blue
a bouquet of 15 flowers, 6 pink and 9 blue
a bouquet of 18 flowers, 12 pink and 6 blue

a bouquet of 18 flowers, 12 pink and 6 blue is correct.

Step-by-step explanation:

Step 1: Find the total number of children.

Number of boys = 2

Total number of children = 3 x number of boys

Total number of children = 3 x 2 = 6

Step 2: Find the ratio of girls to boys

Number of girls = total number of children - total number of boys

Number of girls = 6 - 2 = 4

Girls : Boys

4 : 2

2 : 1

Step 3: Find the ratio of pink and blue flowers

Pink : Blue = Girls : Boys = 2 : 1

Step 4: Check the statements. The ratio of Pink : Blue should be 2 : 1.

1) a bouquet of 12 flowers, 4 pink and 8 blue. Incorrect because in this statement the ratio of pink : blue is 4 : 8 = 1 : 2 instead of 2 : 1.

2) a bouquet of 14 flowers, 8 pink and 6 blue. Incorrect because in this statement the ratio of Pink : Blue 8 : 6 = 4 : 3.

3) a bouquet of 15 flowers, 6 pink and 9 blue  Incorrect because in this statement the ratio of pink : blue is 6 : 9 = 2 : 3.

4) a bouquet of 18 flowers, 12 pink and 6 blue. This is correct because the ratio of pink : blue is 12 : 6 = 2 : 1.

!!                        

A bouquet of 12 flowers, 4 pink and 8 blue

Step-by-step explanation:

Let

x> the number of boys

y ---> the number of girls

z ---> the number of children

we know that

x=2 boys> equation A

z=3x> z=3(2)=6 children > equation B

z=x+y > equation C

substitute the value of x and the value of z in the equation C and solve for y

6=2+y

y=6-2=4 girls

so

The ratio of girls to boys is equal to

2/4=1/2

therefore

The ratio of pink flowers to blue flowers is equal to 1/2

Let

a > the number of pink flowers

b > the number of blue flowers

so

For b=9  blue carnations > Find the value of a

1/2=a/b

1/2=a/9

a=4.5 pink carnations > It doesn't make sense (must be a integer)

For b=8  blue carnations > Find the value of a

1/2=a/b

1/2=a/8

a=4 pink carnations > It makes sense

therefore

A bouquet of 12 flowers, 4 pink and 8 blue

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation