1. Using the information from the previous slide, complete the - PowerPoint PPT Presentation

D AY 83 – B USINESS P ROJECT

W ORD P ROBLEM Mrs. Smith decided to purchase candy for her whole class as a treat. She bought Smarties and Dum-Dum lollipops as “brain food” for their next exam. Each bag of Smarties cost $7.00 (including tax). The bag of Dum-Dum lollipops cost $8.50 (including tax). She ended up spending $60.50 on her purchase of 8 items.

1. Using the information from the previous slide, complete the following table: Number of Smarties Number of Dum- Total Cost for 8 Bags Dum lollipops Bags Items ($) 0 1 2 3 4 5 6 7 8 2. Circle the row that has a total cost of $60.50.

1. Using the information from the previous slide, complete the following table: Number of Smarties Number of Dum- Total Cost for 8 Bags Dum lollipops Bags Items ($) 0 8 $68.00 1 7 $66.50 2 6 $65.00 3 5 $63.50 4 4 $62.00 5 3 $60.50 6 2 $59.00 7 1 $57.50 8 0 $56.00 2. Circle the row that has a total cost of $60.50.

3. How many bags of Smarties did Mrs. Smith buy? 4. How many bags of Dum-Dum lollipops did Mrs. Smith buy? 5. Define your variables.

3. How many bags of Smarties did Mrs. Smith buy? 5 4. How many bags of Dum-Dum lollipops did Mrs. Smith buy? 3 5. Define your variables. x = number of Smarties bags y = number of Dum-Dum lollipop bags

6. Write a system of equations to model the situation.

6. Write a system of equations to model the situation.  y  8 Items: x   Cost: 7 . 00 8 . 50 60 . 50 x y

7. How many bags of Smarties did Mrs. Smith buy?

7. How many bags of Smarties did Mrs. Smith buy? Finding the number of Smarties bags means I should eliminate y since that is the variable that defines Dum-Dum lollipop bags.  y  8 x (multiply this equation by -8.50 to eliminate y)     8 . 50 8 . 50 68 x y   7 . 00 8 . 50 60 . 50 x y   7 . 00 8 . 50 60 . 50 (nothing needs to change here) x y   1 . 50 7 . 50 x     5 1 . 50 1 . 50 x

8. How many bags of Dum-Dum lollipops did Mrs. Smith buy?

8. How many bags of Dum-Dum lollipops did Mrs. Smith buy? Finding the number of Dum-Dum lollipop bags means I should eliminate x since that is the variable that defines Smarties bags.  y  8 x (multiply this equation by -7.00 to eliminate x)     7 . 00 7 . 00 56 x y   7 . 00 8 . 50 60 . 50 x y   7 . 00 8 . 50 60 . 50 (nothing needs to change here) x y   1 . 50 4 . 50 y     3 1 . 50 1 . 50 y

S OLVE    1 3 10 x y    2  2 15 x y

A NSWER K EY Multiply each side of Equation 1 by ─1.     Now the coefficients of these 3 10 1 x y y terms are additive  inverses, 2 15 x y  2  5 x   5 3 Substitute x = ─ 5 in x Equation 1 or in Equation 2.   2 15 2 x y    2 ( 5 ) 15 y  25 4 The check is left for you. y

S OLVE 1     2 3 1 x y     2  5 2 12 x y

A NSWER K EY Multiply each side of Equation 1 by 2 and multiply each side of Equation 2 by 3. Then the y terms will be additive inverses of each other    2(2x + 3y) = 2(─1) 4 6 2 x y   15 6 36 3(5x ─ 2y) = 3(─12) x y   19 38 x Substitute x = ─ 2 in   2 3 x Equation 1    2 3 1 1 x y     2 ( 2 ) 3 1 y  3 3 y The check is left for  you. 1 4 y