SAT Math Practice Q4 - Systems of Linear Equations Word Problems

Here's an SAT math question for you to try. Ana decided to open a bakery that sells brownies and lemon tarts. During her first day of business, she earned 300 dollars by selling 15 brownies and 10 lemon tarts. During her second day, she earned 831 dollars by selling 24 brownies and 55 lemon tarts. What is the price of her brownies? Let the price of each brownie be x. And let the price of each lemon tart be y. On her first day, her total sales were 300 dollars. She earned this by selling 15 brownies and 10 lemon tarts. The price of 15 brownies will be 15x. And the price of 10 lemon tarts will be 10y. Her total sales were 300. So, 15x plus 10y will be equal to 300. This gives us equation one. Similarly, we will make the equation for the second day. The price of 24 brownies will be 24x. And the price of 55 lemon tarts will be 55y. Her total sales were 831. So, 24x plus 55y is equal to 831. This gives us equation two. We need to find the price of a brownie. So we have to find the value of x. To do this, we will equalize the y terms. We will multiply the first equation by 55. And we will multiply the second equation by 10. Let us do the calculations. 15 into 55 gives us 825x. Plus 10 into 55 gives us 550y. Then 300 into 55 is 16,500. Now multiplying the second equation by 10. This gives us 240x plus 550y is equal to 8,310. And now we subtract the two equations. Let's subtract them. The 550y terms will get canceled out. So we have 825 minus 240. Which is 585. So we get 585x. Now, 16,500 minus 8,310 is 8,190. So 585x is equal to 8,190. From here, we can find the value of x. x will be 8,190 divided by 585. Dividing by 585 gives us 14. So the price of a brownie is 14 dollars. The correct answer here is 14.