Question

Singh had $250. He started to spend $15 a week. Singh will have S dollars after t weeks. Jane had $130 at the beginning. She started to save $5 a week. Jane will have I dollars after t weeks. (1) Setup two equations in term of t (week), (2) Determine the number of weeks that both has the same amount of money. (3) Determine the number of the first week that Jane has more money than Singh.

Answer 1

Singh's equation: S=250−15t Jane's equation: I=130+5t

After 6 weeks

5 weeks

**1. Set up two equations**

Let S be the amount of money Singh has after t weeks and let I be the amount of money Jane has after t weeks.

* Singh's equation: $S = 250 - 15t$

* Jane's equation: $I = 130 + 5t$

**2. Determine the number of weeks that both has the same amount of money**

To find the number of weeks that both have the same amount of money, we need to set the two equations equal to each other and solve for t.

```

250 - 15t = 130 + 5t

120 = 20t

t = 6

```

Therefore, both Singh and Jane will have the same amount of money after **6 weeks**.

**3. Determine the number of the first week that Jane has more money than Singh**

To find the number of the first week that Jane has more money than Singh, we need to find the week when I > S.

```

130 + 5t > 250 - 15t

0 > 20t - 120

120 > 20t

t < 6

```

Therefore, Jane will have more money than Singh for the first **5 weeks**.

**Answer:**

1. Singh's equation: $S = 250 - 15t$

Jane's equation: $I = 130 + 5t$

2. After 6 weeks

3. 5 weeks