Question 478546
Let the larger number be a and the smaller number, b.
1) {{{a*b = 3200}}} "The product of two numbers is 3200."
2) {{{a/b = 2}}} "...and the quotient when the larger number is divided by the smaller is 2."
Rewrite equation 2) as:
2a) {{{a = 2b}}} and substitute this for a in equation 1).
1a) {{{2b*b = 3200}}} Simplify.
1b) {{{2b^2 = 3200}}} Divide both sides by2.
1c) {{{b^2 = 1600}}} Take the square root of both sides.
1d) {{{highlight(b = 40)}}} Substitute this value for b in equation 2a).
{{{a = 2(40)}}}
{{{highlight(a = 80)}}}
The two numbers are: 80 and 40.