Question

the color of paint used to paint a race car includes a mixture of yellow and green paint. scotty wants to lighten the color by increasing the amount of yellow paint 30%. if the new mixture contains 3.9 litres of yellow paint, how many litres of yellow paint did he use in the previous mixture

Answer 1

Scotty's original mixture contained 3 litres of yellow paint before he increased it by 30% to get 3.9 litres in the new mixture.

Step-by-step explanation:

The question asks how many litres of yellow paint were used in a previous mixture before Scotty decided to increase the amount of yellow paint by 30% to achieve a total of 3.9 litres in the new mixture. To find the original amount, we need to calculate the base amount that, when increased by 30%, results in 3.9 litres.

We can use the following equation to determine the original amount of yellow paint (let's call it 'y'): y + 0.30y = 3.9 litres. Simplifying this equation, we get 1.30y = 3.9 litres. To find the value of y, we divide both sides by 1.30, giving us y = 3.9 / 1.30 litres. Doing the math, y equals 3 litres. Therefore, Scotty used 3 litres of yellow paint in the original mixture.

Answer 2

let's say he had "x" liters, thus "x" is the 100% then.

then he increased the amount by 30% of that, so the new amount is really 100% + 30%, or 130%, which we know is 3.9 liters of yellow paint.

now, if 3.9 is the 130%, what is "x" anyway?


`\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 3.9&130 \end{array}\implies \cfrac{x}{3.9}=\cfrac{100}{130}\implies x=\cfrac{3.9\cdot 100}{130}`