Cedric cashed a $125 check at the bank. The teller gave Cedric his money in $5 and $10 bills only. If the teller gave Cedric twice as many $10 bills as $5 bills, how many of each type did cedric receive?
Lefkios went to a fast food restaurant for breakfast. He ate an egg sandwich and 2 hash browns for a total of 550 calories. If an egg sandwich has 3 times as many calories as one hash brown, how many calories are in each?
1. Let x = # of $5, then 2x = # of $10
5x + 2(10x) = 125
Solve for x, then 2x
2. Let x = hash brown calories, then egg = 3x
2x + 3x = 550
To solve the first problem, let's represent the number of $5 bills Cedric received as "x". Since the teller gave him twice as many $10 bills as $5 bills, Cedric received 2x $10 bills.
The value of one $5 bill is $5, and the value of one $10 bill is $10. So, we can write the equation:
5x + 10(2x) = 125
Simplifying the equation:
5x + 20x = 125
25x = 125
Divide both sides by 25:
x = 5
Therefore, Cedric received 5 $5 bills and 10(2)(5) = 100 $10 bills.
To solve the second problem, let's represent the number of calories in one hash brown as "x". Since the egg sandwich has 3 times as many calories as one hash brown, the number of calories in the egg sandwich is 3x.
According to the problem, Lefkios ate an egg sandwich and 2 hash browns for a total of 550 calories. So we can write the equation:
3x + 2x = 550
Simplifying the equation:
5x = 550
Divide both sides by 5:
x = 110
Therefore, one hash brown contains 110 calories, and the egg sandwich contains 3(110) = 330 calories.