Question

Mrs. Reyes had some apples. If she gave each student 3 apples, she would have 2 apples left have. If she gave each students 4 apples each she would be 2 short. How many apples did she have.

Answer 1

14 apples

Explanation:

Let x = number of students

Let y = total number of apples

Create a system of equations with the given information.

Equation 1

If she gave each student 3 apples, she would have 2 apples left:

⇒ y - 3x = 2

Equation 2

If she gave each students 4 apples each she would be 2 short:

⇒ y - 4x = -2

Rewrite Equation 1 to make y the subject:

⇒ y = 2 + 3x

Substitute this into Equation 2 and solve for x:

⇒ (2 + 3x) - 4x = -2

⇒ 2 + 3x - 4x = -2

⇒ 2 - x = -2

⇒ -x = -4

⇒ x = 4

Substitute the found value of x into the rewritten Equation 1 and solve for y:

⇒ y = 2 + 3(4)

⇒ y = 2 + 12

⇒ y = 14

Therefore, Mrs Reyes had 14 apples.

Answer 2

• 14 apples

Explanation:

Let

• Number of apples = a
• Number of students = s

According to question we have equations

• a = 3s + 2
• a = 4s - 2

Find the number of students by substitution

• 3s + 2 = 4s - 2
• 4s - 3s = 2 + 2
• s = 4

Find the number of apples

• a = 3*4 + 2 = 12 + 2 = 14