Question 466527
Let the two numbers be a and b, then from the problem description, you can write:
1) {{{b = 3a+5}}} "The second number (b) is five more than three times the first number (a)".
2) {{{a+b = 19}}} "The sum of the numbers is 19." Into this equation, substitute {{{b = 3a+5}}} from equation 1) to get:
3) {{{a+(3a+5) = 19}}} Simplify.
4) {{{4a+5 = 19}}} Subtract 5 from both sides.
5) {{{4a = 14}}} Divide both sides by 4.
6) {{{highlight(a = 3.5)}}} Now substitute this value of a into equation 1) to find the value of b.
7) {{{b = 3(3.5)+5}}} Simplify.
8) {{{b = 10.5+5}}}
9) {{{highlight_green(b = 15.5)}}}
The two rational numbers (not integers!) are: 3.5 and 15.5