Answer:
Number of red buttons = 40
Step-by-step explanation:
red : blue = 5:3
blue : green = 1:2
Green is 48.
We find blue first.
blue : green = blue / green
1:2 = 1/2
b - blue
1/2 = b/48
Cross multiply
48 × 1 = 2 × b
48 = 2b
48 ÷ 2 = b
24 = b
Blue : Green = 24 : 48
Now we find red.
red : blue = red / blue
5 : 3 = 5 / 3
r - red
5/3 = r/24
Cross multiply.
5 × 24 = 3 × r
120 = 3r
120 ÷ 3 = r
40 = r
The ratio will remain the same for the two numbers. Then the number of red buttons is 40.
A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given
The ratio of red buttons and blue buttons is 5:3.
The ratio of blue buttons and green buttons is 1:2.
There are 48 green buttons in the box.
Let x be the red button and y be the blue button.
The number of blue buttons is given by
[tex]\rm \dfrac{y}{48} = \dfrac{1}{2}\\\\y \ \ = \dfrac{48}{2}\\\\y \ \ = 24[/tex]
The number of red buttons is given by
[tex]\rm \dfrac{x}{y} = \dfrac{5}{3}\\\\x \ = \dfrac{5* y}{3}\\\\x \ = \dfrac{5*24}{3}\\\\x \ = 40[/tex]
Thus, the number of red buttons is 40.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
