Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers? Choices
A) 21, 12 B) 9, 0 C) 15, 6 D) 10, 1 E) 14, 5
the larger number: x   the smaller number: y   twice the larger: 2x   three more than five times the smaller: 5y + 3   relationship between ("is"): 2x = 5y + 3   four times the larger: 4x   three times the smaller: 3y   relationship between ("sum of"): 4x + 3y = 71   Now I have two equations in two variables:   2x = 5y + 3   4x + 3y = 71   I will solve, say, the first equation for x:   x = (5/2)y + (3/2)   Then I'll plug the right-hand side of this into the second equation in place of the "x":   4[ (5/2)y + (3/2) ] + 3y = 71   10y + 6 + 3y = 71   13y + 6 = 71   13y = 65   y = 65/13= 
<gadget id="calculator">65/13</gadget>
<output>5</output>
5   Now that I have the value for y, I can solve for x:   x= (5/2)y + (3/2)   x = (5/2)(5) + (3/2)   x = (25/2) + (3/2)   x = 28/2= 
<gadget id="calculator">28/2</gadget>
<output>14</output>
14   Answer: 14, 5
<result>E</result>
Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers?