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EXAMPLE 3

EXAMPLE 3. Standardized Test Practice. SOLUTION. Write verbal models for this situation. EXAMPLE 3. Standardized Test Practice. Equation 1. Equation 2. Write a system of equations. STEP 2. EXAMPLE 3. Standardized Test Practice. Equation 1. 5 x + 7 y = 2500.

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EXAMPLE 3

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  1. EXAMPLE 3 Standardized Test Practice SOLUTION Write verbal models for this situation.

  2. EXAMPLE 3 Standardized Test Practice Equation 1 Equation 2

  3. Write a system of equations. STEP 2 EXAMPLE 3 Standardized Test Practice Equation 1 5x + 7y = 2500 Total cost for all T-shirts 8x + 12y = 4200 Equation 2 Total revenue from all T-shirts sold Solve the system using the elimination method. STEP 3 Multiply Equation 1 by –8 and Equation 2 by 5 so that the coefficients of xdiffer only in sign. 5x + 7y = 2500 – 40x– 56y = – 20,000 40x+ 60y = 21,000 8x + 12y = 4200 Add the revised equations and solve for y. 4y = 1000 y= 250

  4. ANSWER The correct answer is C. EXAMPLE 3 Standardized Test Practice Substitute the value of yinto one of the original equations and solve for x. 5x + 7y= 2500 Write Equation 1. 5x + 7(250) = 2500 Substitute 250 for y. 5x + 1750 = 2500 Simplify. x = 150 Solve for x. The school sold 150 short sleeve T-shirts and 250 long sleeve T-shirts.

  5. 4. WHAT IF? In Example 3, suppose the school spends a total of $3715 on T-shirts and sells all of them for $6160. How many of each type of T-shirt are sold? ANSWER The school sold 365 short sleeve T-shirts and 270 long sleeve T-shirts. for Example 3 GUIDED PRACTICE

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