Question

The countries with the most widgets in the world are the United States and France. If the United States has 2006 more widgets than France and the total number of widgets is 8306. Find the number of widgets for each country.

Answer 1

Given:

a.) The United States has 2006 more widgets than France.

b.) The total number of widgets is 8306.

Let,

x = The number of widgets the United States has

y = The number of widgets France have

x = y + 2006 ; Since the United States has 2006 more widgets than France.

From the given scenario, we generate the following equation:

`\text{ x + y = 8306}`

Let's determine the value of x and y.

`\text{ x + y = 8306}`
`\text{ (}y+2006)\text{ + y =8306}`
`\text{ }y+2006\text{ + y =8306}`
`\text{ }y+\text{ y =8306 - }2006`
`\text{ 2y = }6,300`
`\text{ }\frac{\text{2y}}{2}\text{ = }(6,300)/(2)`
`\text{ y = }3150`

Therefore, France has 3150 Widgets.

Let's determine the number of fidgets the United States has. Use y = 3150 in the equation x + y = 8306.

`x+y=8306`
`x+3150=8306`
`x=8306\text{ - }3150`
`x=5156`

Therefore, the United States has 5156 Widgets.