bryon found that one dozen eggs weighed the same as 5 apples. He also found that 2 eggs and 22grams weighed the same as 1 apple. Find the mass of an egg and an apple
Let's use a system of equations to solve for the mass of an egg and an apple.
Let e be the mass of one egg in grams and a be the mass of one apple in grams.
From the first piece of information, we know that:
12e = 5a
From the second piece of information, we know that:
2e + 22 = a
Now we can use substitution to solve for e or a.
Let's solve for a in terms of e from the second equation:
a = 2e + 22
Now we can substitute this expression for a into the first equation:
12e = 5(2e + 22)
Simplifying this equation we get:
12e = 10e + 110
2e = 110
e = 55
So the mass of one egg is 55 grams.
Now we can use this value to find the mass of one apple:
a = 2e + 22 = 2(55) + 22 = 132
So the mass of one apple is 132 grams.
Therefore, the mass of an egg is 55 grams and the mass of an apple is 132 grams.
Let's use algebra to solve this problem step-by-step.
1. Let's assign variables to the unknown masses. Let's call the mass of an egg "E" and the mass of an apple "A".
2. From the first statement, Bryon found that 1 dozen (which is 12) eggs weighed the same as 5 apples, so we can write the equation:
12E = 5A (Equation 1)
3. From the second statement, Bryon found that 2 eggs and 22 grams weighed the same as 1 apple, so we can write the equation:
2E + 22 = A (Equation 2)
4. Now we have a system of equations with two unknowns. We can solve it using substitution or elimination. Let's use substitution:
- Solve Equation 2 for A:
A = 2E + 22
- Substitute this value of A into Equation 1:
12E = 5(2E + 22)
5. Simplifying the equation:
12E = 10E + 110
6. Rearranging the equation:
12E - 10E = 110
2E = 110
7. Solving for E:
E = 110/2
E = 55 grams
8. Now, substitute the value of E into Equation 2 to find A:
A = 2(55) + 22
A = 110 + 22
A = 132 grams
Therefore, the mass of an egg is 55 grams, and the mass of an apple is 132 grams.