Answer:
9 cans of soup and the 4 frozen dinners were purchased
Step-by-step explanation:
Let x represent the number of cans of soup purchased.
Let y represent the number of frozen dinners purchased.
Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that
x + y = 13
Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. The 13 cans of soup and frozen dinners which he purchased collectively contain 4450 mg of sodium. This means that
250x + 550y = 4450 - - - - - - - - -1
Substituting x = 13 - y into equation 1, it becomes
250(13 - y) + 550y = 4450
3250 - 250y + 550y = 4450
- 250y + 550y = 4450 - 3250
300y = 1200
y = 1200/300
y = 4
Substituting y = 4 into x = 13 - y, it becomes
x = 13 - 4 = 9
The polynomial whose zeroes are 1, 2 and 3 is given by,
(x-1)(x-2)(x-3) = 0
(x-1)[x²-3x-2x+6]=0
(x-1)[x²-5x+6]=0
x[x²-5x+6] -1[x²-5x+6]=0
x³-5x²+6x-x²+5x-6=0
x³-6x²+11x-6=0
Therefore, the required polynomial is,
x³ - 6x² + 11x -6 = 0
