Answer: One hotdog contains 150 calories, and one cottage cheese contains 220 calories.
Step-by-step explanation: The unknowns which are hotdogs and cottage cheese shall be represented as hotdogs as ‘d’ and cottage cheese as ‘c.’
So if 2 hotdogs and 3 cottage cheese contains 960 calories, this can be expressed as 2d + 3c = 960. Also if 5 hotdogs and 2 cottage cheese contains 1190 calories, this can as well be written as 5d + 2c = 1190.
We now have a pair of simultaneous equations which are
2d + 3c = 960 ———(1)
5d + 2c = ———(2)
We shall use the elimination method to solve this. Multiply equation (1) by 2 and multiply equation (2) by 3
Then we now have;
4d + 6c = 1920 ———(3)
15d + 6c = 3570 ———(4)
Subtract equation (3) from equation (4)
11d = 1650
Divide both sides of the equation by 11
d = 150
Substitute for the value of d into equation (1)
2d + 3c = 960
2(150) + 3c = 960
300 + 3c = 960
Subtract 300 from both sides of the equation
3c = 660
Divide both sides of the equation by 3
c = 220.
Therefore, one hotdog (d) contains 150 calories and one cottage cheese (c) contains 220 calories.
