Question 4. Pranav wants to write a number at each vertex and on each edge of the rhombus shown. He wants the sum of the numbers at the two vertices at the ends of each edge to be equal to the number written on the edge. What number will he write instead of the question mark? Take a look at our shape. Enable the numbers in the vertices as A, B, C, and D. This we can start writing out our formulas. We know that A plus B will give us 9, B plus C will give us 13, C and D are unknown, and D and A give us 8. Now, through this we know that A plus B plus C plus D is going to equal 13 and 18 because B and C is 13 and A and D is 8, so we can write that out like so. Now, if we take a look at our first formula, A plus B equals 9, we can substitute that into our larger formula and get D plus 9 plus C equal to 21. If we subtract 9 from both sides, we'll get what D plus C equals, which is what we want to find out. When we get D plus C equals 12, that gives us our answer, which is B, 12.

rhombus

vertex numbers

edge sum

equation solving

geometry problem