Tight Knit is an online store that sells two different tiers of monthly subscription boxes with knitting supplies. Recently, the number of basic subscriptions has been decreasing by 5 each month, while the number of deluxe subscriptions has been increasing by 8 each month. This month, the company had 288 basic subscriptions and 93 deluxe subscriptions.

Question

How many months will it take for the number of basic subscriptions to match the number of deluxe subscriptions?
months

Answer 1

Let's denote the number of months from now as \( x \).

Currently, Tight Knit has:

• Basic subscriptions: 288
• Deluxe subscriptions: 93

According to the problem:

• The number of basic subscriptions decreases by 5 each month, so after \( x \) months, the number of basic subscriptions will be \( 288 - 5x \).
• The number of deluxe subscriptions increases by 8 each month, so after \( x \) months, the number of deluxe subscriptions will be \( 93 + 8x \).

We want to find \( x \) when the number of basic subscriptions equals the number of deluxe subscriptions: \[ 288 - 5x = 93 + 8x \]

Now, let's solve for \( x \):

1. Rearranging the equation: \[ 288 - 93 = 8x + 5x \] \[ 195 = 13x \]

2. Dividing both sides by 13: \[ x = \frac{195}{13} = 15 \]

So, it will take 15 months for the number of basic subscriptions to match the number of deluxe subscriptions.