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:
[tex]\text{ x + y = 8306}[/tex]Let's determine the value of x and y.
[tex]\text{ x + y = 8306}[/tex][tex]\text{ (}y+2006)\text{ + y =8306}[/tex][tex]\text{ }y+2006\text{ + y =8306}[/tex][tex]\text{ }y+\text{ y =8306 - }2006[/tex][tex]\text{ 2y = }6,300[/tex][tex]\text{ }\frac{\text{2y}}{2}\text{ = }\frac{6,300}{2}[/tex][tex]\text{ y = }3150[/tex]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.
[tex]x+y=8306[/tex][tex]x+3150=8306[/tex][tex]x=8306\text{ - }3150[/tex][tex]x=5156[/tex]Therefore, the United States has 5156 Widgets.