Matt bought some Dino Brand and Lion Brand correction tapes at the prices shown below. $\frac{1}{3}$ of the correction tapes Matt bought was Lion Brand correction tapes. He spent $198 more on Dino Brand correction tapes. How much did he spend on the correction tapes? Ans : ___

1. Determine the ratio of the number of Lion Brand to Dino Brand tapes.

Since $\frac{1}{3}$ of the tapes were Lion Brand, the remaining $1 - \frac{1}{3} = \frac{2}{3}$ were Dino Brand.
Ratio of Lion Brand to Dino Brand tapes = $1 : 2$.

2. Define a 'set' of tapes that maintains the ratio and is easily divisible by the bundle sizes.

Lion Brand tapes are sold in bundles of 3, and Dino Brand in bundles of 4. To easily calculate costs, we find a common multiple for the quantities.
Let one 'set' consist of $12$ Lion Brand tapes (which is $4$ bundles of $3$).
To maintain the $1 : 2$ ratio, the set must contain $12 \times 2 = 24$ Dino Brand tapes (which is $6$ bundles of $4$).

3. Calculate the cost and the difference in cost for one such set.

Cost of $12$ Lion Brand tapes = $4 \times \char36{}7.25 = \char36{}29$
Cost of $24$ Dino Brand tapes = $6 \times \char36{}8.50 = \char36{}51$
Difference in cost for one set = $\char36{}51 - \char36{}29 = \char36{}22$

4. Find the number of sets and the total amount spent.

Number of sets = $198 \div 22 = 9$
Total cost for one set = $\char36{}29 + \char36{}51 = \char36{}80$
Total amount spent = $9 \times \char36{}80 = \char36{}720$