Question

Sandy has four boxes filled with pink ribbons and yellow ribbons. The table shows the number of pink and yellow ribbons in each box. Box Number Pink Ribbons Yellow Ribbons 1 4 5 2 16 20 3 12 15 4 36 45

A fifth box has pink and yellow ribbons in the same proportion as Sandy's first four boxes. Which table could represent box number 5?

Answer 1

Given : Sandy has four boxes filled with pink ribbons and yellow ribbons.

Box No. Pink Ribbons Yellow Ribbons

1 4 5

2 16 20

3 12 15

4 36 45

To Find : Relation between Pink Ribbons and Yellow Ribbons

Solution:

Pink Ribbons = x

Yellow Ribbons = Y

Box No. Pink Ribbons x Yellow Ribbons y

1 4 5

2 16 20

3 12 15

4 36 45

Slope = (20 - 5)/(16 - 4)

= 15/12

=5/4

y - 5 = (5/4)(x- 4)

=> 4y - 20 = 5x - 20

=> 4y = 5x

=> 5x = 4y

5x = 4y is the relations between Pink Ribbons and Yellow Ribbons

Answer 2

Explanation:

Box Number 5 should have 48 pink ribbons and 60 yellow ribbons. We can calculate this by first adding up the total number of pink and yellow ribbons in Sandy's first four boxes (4+16+12+36 = 68 pink ribbons, and 5+20+15+45 = 85 yellow ribbons). The ratio of pink to yellow ribbons in the first four boxes is 68:85, or 4:5.

To determine the amount of pink and yellow ribbons in Box Number 5, we can use the ratio from the first 4 boxes by multiplying 4 and 5 by any factor that will give us integers. This factor is 8, so we get 4 x 8 = 32 pink ribbons and 5 x 8 = 40 yellow ribbons, for a total of 48 pink ribbons and 60 yellow ribbons in Box Number 5.