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On the very good chance that the person answering this question doesn't have lessons 17 and 18, it would help the question to be answered if you would write out the actual problems.

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Q: What are the answers to lessons 17 and 18 in hands on equations?
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If the sum of two numbers is 17 and the sum of their square is 145 - what is the larger number?

This information gives us the equations: x + y = 17 x2 + y2 = 145 These equations are more difficult to solve. The solution to the equations is below. Possibly easier (at least with this specific question) is guessing and checking. The answers are 8 and 9. To check: 8 + 9 = 17 64 + 81 = 145 === === The equations we have are: x + y = 17 x2 + y2 = 145 Lets substitue by using the first equation: x = -y + 17 plug that in: (-y + 17)2 + y2 = 145 Now simplify: y2 - 34y + 289 + y2 = 145 Simplify a little more: 2y2 - 34y + 289 = 145 Create a quadratic equation: 2y2 - 34y + 144 = 0 Factor the polynomial (or use the quadratic formula): (y - 9)(2y - 16) = 0 So either: y - 9 = 0 so y = 9, Or 2y - 16 = 0 so y = 8. Note: Because both equations are symmetric (meaning x and y can be switched without changing anything, like x + y = 17 is the same as y + x = 17), we know that x and y are each either 8 or 9. Either way the answers are 8 and 9. Plug these into the original equations and they work. Otherwise, just plug the y values into the easiest equation to solve for x. So x + 8 = 17 so x = 9. The other option is x + 9 = 17 which leads to x = 8. The answers are (8,9) and (9,8). Either way, the two numbers to fill the requirements are 8 and 9.


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If the sum of two numbers is 17 and the sum of their square is 145 - what is the larger number?

This information gives us the equations: x + y = 17 x2 + y2 = 145 These equations are more difficult to solve. The solution to the equations is below. Possibly easier (at least with this specific question) is guessing and checking. The answers are 8 and 9. To check: 8 + 9 = 17 64 + 81 = 145 === === The equations we have are: x + y = 17 x2 + y2 = 145 Lets substitue by using the first equation: x = -y + 17 plug that in: (-y + 17)2 + y2 = 145 Now simplify: y2 - 34y + 289 + y2 = 145 Simplify a little more: 2y2 - 34y + 289 = 145 Create a quadratic equation: 2y2 - 34y + 144 = 0 Factor the polynomial (or use the quadratic formula): (y - 9)(2y - 16) = 0 So either: y - 9 = 0 so y = 9, Or 2y - 16 = 0 so y = 8. Note: Because both equations are symmetric (meaning x and y can be switched without changing anything, like x + y = 17 is the same as y + x = 17), we know that x and y are each either 8 or 9. Either way the answers are 8 and 9. Plug these into the original equations and they work. Otherwise, just plug the y values into the easiest equation to solve for x. So x + 8 = 17 so x = 9. The other option is x + 9 = 17 which leads to x = 8. The answers are (8,9) and (9,8). Either way, the two numbers to fill the requirements are 8 and 9.


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