When you plug this in to the second equation, you get: Since V is likely easier to work with in the second equation (the substituted term is likely easier to multiply by 1.5 than by 1.25), you can leverage the first equation to get P in terms of V: This problem sets up nicely for using the Substitution Method for systems of equations.
Then for the money, the total revenue will be a combination of how much was made from selling vegetarian slices ($1.25 times the number of vegetarian) and how much was made from selling pepperoni ($1.50 times the number of pepperoni). If you use V to represent the number of vegetarian slices and P to represent the number of pepperoni slices, you can express the total number of slices as: This problem provides you with the opportunity to set up two equations: the total number of slices of pizza, and the total amount of money. That means that R = 48, but remember in Systems of Equations problems to always check that your algebra has answered the specific question, as a problem with two variables allows you to mistakenly solve for the wrong one! The question asks you about Spot's weight, so you can subtract 9 from 48 to see that Spot weighs 39 pounds. If you structure it that way, you can stack the equations and sum them: The equation with subtraction allows you to go straight into the Elimination Method as you have a + S in the first equation and a -S in the second, so that may be your preferred choice. Another way is to see that Rover weighs more, and the difference is 9, meaning that R - S = 9. One is to say that "Rover's weight is 9 pounds more than Spot's weight" and then use the fact that "is" means "equals" so that the words translate directly to the equation: R = 9 + S.
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Then if Rover weighs 9 pounds more than Spot, you have a few choices for how to express that. R + S = 87 (in which R = Rover's weight and S = Spot's weight) If the two dogs weigh a total of 87 pounds, you can express that as: Often on the SAT, these Systems problems will start by giving you a combined total as this one does. This problem provides you with two equations, allowing you to use Systems of Equations logic to solve once you've constructed the equations.
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Then check your work: does Blin's total of $150,000 plus Alex's total of $90,000 arrive at the sum we know to be $240,000? It does, so you can confidently choose $150,000. The question asks you about Blin's total, not Alex's, so you need to add $60,000 to get to Blin's total of $150,000. Of course, at this point you need to check whether you solved for the proper variable. This structure sets up well for Substitution you already have B in terms of A, so you can plug in the second equation for the first: For the relationship equation, you can say that Blin's total is $60,000 more than Alex's, which translates to B = 60,000 + A. The sum equation is generally straightforward you can express that as B + A = 240,000. Here that's Blin raised $60,000 more than Alex did. You're given the sum of two entities - here that's Blin's Total + Alex's Total = $240,000 - and a relationship between those two entities. This problem provides you with a classic SAT Systems of Equations setup.
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