### Video Transcript

A clothing store has a sale on shirts and jeans. Two shirts and three pairs of jeans cost 540 dollars. Three shirts and one pair of jeans cost 420 dollars. How much will a customer who buys five shirts and four pairs of jeans pay?

In this question, weβre given two pieces of information with two unknowns, the cost of a shirt and the cost of a pair of jeans. Therefore, we can set up a pair of simultaneous equations. We can let π₯ be the cost of a shirt. And we can let the latter π¦ be the cost of a pair of jeans. Weβre told that two shirts and three pairs of jeans cost 540 dollars. Therefore, two π₯ plus three π¦ is equal to 540. Three shirts and one pair of jeans cost 420 dollars. Therefore, three π₯ plus π¦ is equal to 420. We now have a pair of simultaneous equations with two unknowns π₯ and π¦.

We would usually solve these using either substitution or elimination. However, in this particular question, thereβs an easier way to solve the problem. Weβre asked to work out how much a customer who buys five shirts and four pairs of jeans would pay. This means that we want to calculate the cost of five π₯ plus four π¦. The π₯-values in our two equations are two π₯ and three π₯. And two π₯ plus three π₯ is equal to five π₯. Likewise, three π¦ plus π¦ is equal to four π¦. Adding equation one and equation two will give us the cost of five π₯ plus four π¦. We need to add 540 and 420. This is equal to 960. Since two shirts and three pairs of jeans cost 540 dollars and 3 shirts and one pair of jeans cost 420 dollars. Then five shirts and four pairs of jeans will cost 960 dollars.

As mentioned earlier, a longer method here would be to work out the value of π₯ and π¦, the cost of one shirt and one pair of jeans. We could then substitute that back into the expression five π₯ plus four π¦. Doing this by either elimination or substitution would also give us a final answer of 960 dollars.