Solving Word
Problems With The
Toy Story Gang !

Using Equations to Solve Problems:
Many problems can be solved by
translating them into mathematical language and so in the following problems we are going to translate a problem into equations!

Word Problem:
One day a store sold 30 sweatshirts. White ones cost $9.95, and yellow ones cost $10.50. In all, $310.60 worth of sweatshirts were sold. How many of each color were sold?

Work:
Since we know that the white shirts + the yellow shirts equal 30 sweatshirts, we can make the equation:
x + y = 30
x = White Shirts
y = Yellow Shirts
For the next equation we know that the total amount was $310.60 and x + y equals this amount so the equation would be:
$9.95x + $10.50y = $310.60
We need one equation to be in the form of y =
so we subtract x from both sides
x + y = 30
y = -x + 30
We now have a system of equations:
y = -x + 30
$9.95x + $10.50y = $310.60
Our next step is....
Substitution
$9.95x + $10.50 (-x + 30) = $310.60
$9.95x - $10.50x + $315 = $310.60
-.55x = - 4.40
x = 8
Now we substitute x in the first equation:
y = -x + 30
y = -8 + 30
y = 22
(8, 22)
We now know that 8 white shirts
were sold and 22 yellow shirts were sold!
Now we can check our answer by...
Substitution
y = -x + 30
22 = -8 + 30
22 = 22
CORRECT !

Here Are Five Practice Word Problems:

Don't Let Go! You Can Do It!

WORD PROBLEM: ANSWER:

1. 8 small boxes plus 5 large boxes cost $184. A large box costs $3 more than a small box. What is the cost of each size box? 1. A large box costs $16, a small box costs $13.

2. Solution A is 2% alcohol. Solution B is 6% alcohol. 60 L of mixture are needed. How many liters of each solution are needed for the mixture to be 3.2% alcohol? 2. The owner should us 42 L of 2% solution and
18 L of 6% solution.

3. The sum of a certain number and a second number is -42. The first number minus the second is 52. Find the numbers. 3. (5, -47)

4. One day a store sold 45 pens, one kind at $8.50 and another kind at $9.75. In all, $398.75 was taken in. How many of each kind were sold? 4. 13 @ $9.75
32 @ $8.50

5. Carlos is 8 years older than his sister Maria. Four years ago Maria was two thirds as old as Carlos. How old are they now? 5. Maria is 20 years old
Carlos is 28 years old

PROBLEM SOLVING GUIDELINES:
1. UNDERSTAND THE PROBLEM

2. DEVELOP AND CARRY OUT A PLAN

3. FIND THE ANSWER AND CHECK

Remember To Always Have A Plan While
Solving Systems Of Equations!

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1. 8 small boxes plus 5 large boxes cost $184. A large box costs $3 more than a small box. What is the cost of each size box?	1. A large box costs $16, a small box costs $13.
2. Solution A is 2% alcohol. Solution B is 6% alcohol. 60 L of mixture are needed. How many liters of each solution are needed for the mixture to be 3.2% alcohol?	2. The owner should us 42 L of 2% solution and 18 L of 6% solution.
3. The sum of a certain number and a second number is -42. The first number minus the second is 52. Find the numbers.	3. (5, -47)
4. One day a store sold 45 pens, one kind at $8.50 and another kind at $9.75. In all, $398.75 was taken in. How many of each kind were sold?	4. 13 @ $9.75 32 @ $8.50
5. Carlos is 8 years older than his sister Maria. Four years ago Maria was two thirds as old as Carlos. How old are they now?	5. Maria is 20 years old Carlos is 28 years old