00:01
In this problem, we have been given information about the calories and grams of carbohydrates in one cup serving of spaghetti and a one cup serving of chopped iceberg lettuce.
00:11
Now, we need to determine how many servings of spaghetti and how many servings of iceberg lettuce would be required to obtain 135 calories and 17 grams of carbohydrates.
00:21
So, let us consider a to be the number of one cup servings of spaghetti.
00:32
And let us consider b to be the number of servings of iceberg lettuce.
00:41
Then first of all, note that one serving of spaghetti with meatballs contains 260 calories.
00:47
So a servings will have 260 times a calories.
00:52
And a one cup serving of chopped iceberg lettuce has five calories.
00:57
So b servings will have five times b calories.
01:00
So the total number of calories will be obtained by adding these two, and it is said that we want a total of 135 calories.
01:08
So we get this equation, 2 .68 plus 5b is equal to 135.
01:12
Now, let us consider the carbohydrates.
01:15
Now, there are 32 grams of carbohydrates in a serving of spaghetti.
01:18
So in a servings, we'll have 32a, and one cup serving of chopped iceberg lettuce has one gram of carbohydrates, so 1 times b.
01:30
Just b.
01:31
That will be the amount of carbohydrates in b servings.
01:35
We add these two to obtain the total amount of carbohydrates and we want 17 grams.
01:40
So this is what we get.
01:41
So we need to solve these two equations for the values of a and b.
01:45
So what we're going to do is 1 minus 5 times equation 2.
01:50
If we do that, first of all, write the left -hand side of equation 1 and from that we subtract five times the left -hand side of equation two.
02:00
So five times 32a, that's 160a plus 5 times b...