9514 1404 393
Answer:
- hat = 5
- pumpkin = 2
- ghost = 7
- cauldron = 10
Step-by-step explanation:
Using h, p, g, c to represent the values of the hat, pumpkin, ghost, and cauldron, respectively, we can write 5 equations:
- gh +h = 40
- cp +p = 22
- g +2c = 27
- ph +g = 17
- 2g +h = 19
Solving the last equation for h, and substituting into the first equation gives ...
h = 19 -2g
g(19 -2g) +(19 -2g) = 40
2g^2 -17g +21 = 0 . . . . . . . . write in standard form
(2g -3)(g -7) = 0 . . . . . . . factored form
The values of g that make the factors zero are g = 3/2 and g = 7. If we assume the solution is restricted to integer values, then g = 7, and ...
h = 19 -2·7 = 5
From equation 4, ...
5p +7 = 17 ⇒ p = 2
From equation 3, ...
7 +2c = 27 ⇒ c = 10
The values of the symbols are ...
- hat = 5
- pumpkin = 2
- ghost = 7
- cauldron = 10
_____
Check
Equation 2 becomes ...
10·2 +2 = 22 . . . . . . true
