# Video: US-SAT04S4-Q06-843194103785

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

02:53

### 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, we’re 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 𝑥 be the cost of a shirt. And we can let the latter 𝑦 be the cost of a pair of jeans. We’re told that two shirts and three pairs of jeans cost 540 dollars. Therefore, two 𝑥 plus three 𝑦 is equal to 540. Three shirts and one pair of jeans cost 420 dollars. Therefore, three 𝑥 plus 𝑦 is equal to 420. We now have a pair of simultaneous equations with two unknowns 𝑥 and 𝑦.

We would usually solve these using either substitution or elimination. However, in this particular question, there’s an easier way to solve the problem. We’re 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 𝑥 plus four 𝑦. The 𝑥-values in our two equations are two 𝑥 and three 𝑥. And two 𝑥 plus three 𝑥 is equal to five 𝑥. Likewise, three 𝑦 plus 𝑦 is equal to four 𝑦. Adding equation one and equation two will give us the cost of five 𝑥 plus four 𝑦. 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 𝑥 and 𝑦, the cost of one shirt and one pair of jeans. We could then substitute that back into the expression five 𝑥 plus four 𝑦. Doing this by either elimination or substitution would also give us a final answer of 960 dollars.