Question

A salsa recipe uses green pepper, onion, and tomato in the extended ratio 1:3:9. How many cups of onion are needed to make 117 cups of salsa?

Answer 1

The number of cups of onion that are needed to make 117 cups of salsa is $\boxed{27}.$

Further explanation:

The proportionality equation can be expressed as follows,

$y \propto x$

The value of $y$ changes as $x$ changes. If the value of $x$ increases then the value of $y$ is also increasing.

The inversely proportional relationship can be expressed as,

$y \propto \dfrac{1}{x}$

The equation can be expressed as follows,

$y = kx$

Here, k is the proportionality constant.

Given:

A salsa recipe uses green pepper, onion, and tomato in the extended ratio $1:3:9.$

Explanation:

A salsa recipe uses green pepper, onion, and tomato in the extended ratio $1:3:9.$

Let us consider that the amount of green pepper is $\boxed{1x}.$

Let us consider that the amount of onion is $\boxed{3x}.$

Let us consider that the amount of tomato is $\boxed{9x}.$

The total amount green pepper, onion and tomato can be obtained as follows,

$\begin{aligned}{\text{Total}} &= x + 3x + 9x\\&= 13x\\\end{aligned}$

There are 117 cups of salsa.

The value of $x$ can be obtained as follows,

$\begin{aligned}13x &= 117\\x &= \frac{{117}}{{13}}\\x&= 9\\\end{aligned}$

The amount of onion used to make 117 cups of salsa can be obtained as follows,

$\begin{aligned}{\text{Amount of onion}} &= 3 \times 9\\&= 27\\\end{aligned}$

The number of cups of onion that are needed to make 117 cups of salsa is $\boxed{27}.$

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

Keywords: proportional, salsa, recipe, green pepper, onion, tomato, extended, ratio, 1:3:9, cups, cups of onion, 117 cups, directly proportional, constant, proportionality equation, constant of proportionality.

Answer 2

Green pepper:  1 k
Onion:  3 k
Tomato:  9 k
1 k + 3 k + 9 k = 13 k
k = 117 : 13 = 9
3 k = 3 * 9 = 27 cups of onion.