Question

During its first week of business, a market sold a total of 108 apples and oranges. The second week, five times the number of apples and three times the number of oranges were sold. A total of 452 apples and oranges were sold during the second week. How many more apples than oranges were sold in the first week?

Answer 1

• 20 more apples than oranges were sold in the first week

Step-by-step explanation:

1) First week

• 108 apples and oranges.

• Variables:

number of apples: A

number of oranges: N

• Equation:

A + N = 108 ---------- equation 1

2) Second week

• Five times the number of apples: 5A

• Three times the number of oranges: 3N

• A total of 452 apples and oranges.

• Equation:

5A + 3N = 452 --------- equation 2

3) System of equations

• A + N = 108 ---------- equation 1

• 5A + 3N = 452 --------- equation 2

4) Solve

i) Mutiply the equation 1 by - 3:

• - 3A - 3N = - 324 ---------- equation 1a

ii) Add equations 1a and 2 and simplify:

• 5A - 3A = 452 - 324
• 2A = 128
• A = 64

iii) Substitute the value of A in the equation 1 and solve for N:

• 64 + N = 108

• N = 108 - 64

• N = 44

5) How many more apples than oranges were sold in the first week?

• 64 - 44 = 20 ← answer