Question

Carlos mixed 3 1⁄2 cups of red paint with 4 1⁄2 cups of yellow paint to make an orange paint. How many cups of red paint and how many cups of yellow paint will Carlos need to make 12 cups of the same shade of orange paint? Solve in at least three different ways.

Answer 1

The answer is " red cups is "5.25""

Explanation:

Given:

red paint=
`3(1)/(2)= (7)/(2) =3.5`

yellow paint=
`4(1)/(2)= (9)/(2) =4.5`

total cups=12

i) The Ratio of red and yellow is= 3.5 : 4.5

If the red cups are=
`(3.5)/(8)`

number of red cups:

`\to (3.5)/(8)* 12\\\\\to (3.5)/(2)* 3\\\\\to 3.5* 1.5\\\\\to 5.25`

ii)

`\to 3.5x+4.5x=12......(a)\\\\\to 8x=12\\\to x=(12)/(8)\\\\\to x=(3)/(2)\\\\`

put the value of x in equation (a):

`\to 3.5 * (3)/(2)+4.5* (3)/(2)=12\\\\\to 35 * (3)/(20)+45* (3)/(20)=12\\\\\to 5.25+6.75=12`

iii)

if
`(4.5)/(8) * 12= 6.75` yellow cups used in making orange paint

so, red paint +yellow paint = total cups

let, red paint cups =x

⇒x+6.75=12

⇒x=12-6.75

⇒x=5.25

The value of red cups is 5.25.