Question: 5 John and Tom both collected money for charity on Monday, Tuesday and Wednesday last week. Before they met to check how much they had raised on each of the days, both John and Tom drew pie charts to show the amount that they had collected on each day. The two pie charts are shown below. John Tom Monday Tuesday Wednesday On Monday they collected a total of $30 between them and on Tuesday they collected a total of $40. What is the total amount raised by John over the three days? A $40 B $60 C $80 D $120 John pie chart at center-left: Monday = one quarter, Tuesday = one quarter, Wednesday = one half. Tom pie chart at center-right: Monday = one quarter, Tuesday = three eighths, Wednesday = three eighths.

1. **State the problem:** John and Tom collected money for charity on Monday, Tuesday, and Wednesday. We know the total collected on Monday ($30) and Tuesday ($40). We want to find the total amount John raised over the three days. 2. **Understand the pie charts:** - John's pie chart shows Monday = $\frac{1}{4}$, Tuesday = $\frac{1}{4}$, Wednesday = $\frac{1}{2}$ of his total collection. - Tom's pie chart shows Monday = $\frac{1}{4}$, Tuesday = $\frac{3}{8}$, Wednesday = $\frac{3}{8}$ of his total collection. 3. **Set variables:** Let John's total collection be $J$ and Tom's total collection be $T$. 4. **Use Monday's data:** On Monday, total collected = 30. John's Monday amount = $\frac{1}{4}J$. Tom's Monday amount = $\frac{1}{4}T$. So, $$\frac{1}{4}J + \frac{1}{4}T = 30$$ Multiply both sides by 4: $$J + T = 120$$ 5. **Use Tuesday's data:** On Tuesday, total collected = 40. John's Tuesday amount = $\frac{1}{4}J$. Tom's Tuesday amount = $\frac{3}{8}T$. So, $$\frac{1}{4}J + \frac{3}{8}T = 40$$ Multiply both sides by 8: $$2J + 3T = 320$$ 6. **Solve the system of equations:** From step 4: $$J + T = 120$$ Multiply by 2: $$2J + 2T = 240$$ Subtract this from the equation in step 5: $$2J + 3T = 320$$ $$-(2J + 2T = 240)$$ ------------------- $$T = 80$$ 7. **Find $J$:** From $J + T = 120$: $$J + 80 = 120$$ $$J = 40$$ 8. **Find John's total collection:** John's total is $J = 40$. **Answer: A 40**