example 4
Purchasing
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
Chapter 7.1
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
Total
x  Number
y  of Carsz 
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
Total
Amount
Spendz  200,000
40,000
x  30,000
y to25,000
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
2009 PBLPathways
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
-40,000 E1 + E2  E2
x
y
z
7
 10,000 y  15,000 z  80,000
1
 10,000
E1 + E2  E2
x y
z7
y  1.5 z  8
2009 PBLPathways
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
-40,000 E1 + E2  E2
x
y
z
7
 10,000 y  15,000 z  80,000
1
 10,000
E1 + E2  E2
x y
z7
y  1.5 z  8
2009 PBLPathways
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
-40,000 E1 + E2  E2
x
y
z
7
 10,000 y  15,000 z  80,000
1
 10,000
E1 + E2  E2
x y
z7
y  1.5 z  8
2009 PBLPathways
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
-40,000 E1 + E2  E2
x
y
z
7
 10,000 y  15,000 z  80,000
1
 10,000
E1 + E2  E2
x y
z7
y  1.5 z  8
2009 PBLPathways
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
-40,000 E1 + E2  E2
x
y
z
7
 10,000 y  15,000 z  80,000
1
 10,000
E2  E2
x y
z7
y  1.5 z  8
2009 PBLPathways
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
-40,000 E1 + E2  E2
x
y
z
7
 10,000 y  15,000 z  80,000
1
 10,000
E2  E2
x y
z7
y  1.5 z  8
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Echelon Form
x y
z7
y  1.5 z  8
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Echelon Form
y  8  1.5 z
x7 yz
 7   8  1.5 z   z
x y
z7
y  1.5 z  8
 1  0.5 z
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Echelon Form
y  8  1.5 z
x7 yz
 7   8  1.5 z   z
x y
z7
y  1.5 z  8
 1  0.5 z
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Echelon Form
y  8  1.5 z
x7 yz
 7   8  1.5 z   z
x y
z7
y  1.5 z  8
 1  0.5 z
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Solution
x  1  0.5 z
y  8  1.5 z
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
z
x
y
0
-1
8
1
-0.5
6.5
2
0
5
3
0.5
3.5
4
1
2
5
1.5
0.5
6
2
-1
7
2.5
-2.5
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Solution
x  1  0.5 z
y  8  1.5 z
2009 PBLPathways
A young man wins $200,000 and (foolishly) decides to buy a new car for each of the
seven days of the week. He wants to choose from cars that are priced at $40,000,
$30,000, and $25,000. How many cars of each price can he buy with the $200,000?
x: number of cars costing $40,000
y: number of cars costing $30,000
z: number of cars costing $25,000
z
x
y
0
-1
8
1
-0.5
6.5
2
0
5
3
0.5
3.5
4
1
2
5
1.5
0.5
6
2
-1
7
2.5
-2.5
x
y
z
7
40,000 x  30,000 y  25,000 z  200,000
Solution
x  1  0.5 z
y  8  1.5 z
2009 PBLPathways