Twelve Smooth Guide Pens and eight Easy- Write pencils cost exactly $16.00 at Office world. Six smooth - Glide Pens and ten Esay -write Pencils cost $11.00 at the same location . How much will nine Smooth-Glide pens and nine Easy-Write pencils cost at Office world? (disregard the dollar sign when gridding your answer).

Answer

To solve the problem step by step, we will set up equations based on the information given and then solve for the costs of the Smooth-Glide pens and Easy-Write pencils.

### Step 1: Define Variables
Let:
- \( X \) = cost of one Smooth-Glide pen
- \( Y \) = cost of one Easy-Write pencil

### Step 2: Set Up the Equations
From the problem, we have the following two equations based on the costs provided:
1. \( 12X + 8Y = 16 \) (from the first statement)
2. \( 6X + 10Y = 11 \) (from the second statement)

### Step 3: Simplify the Equations
We can simplify these equations to make calculations easier. Let's keep them as they are for now.

### Step 4: Make Coefficients Equal
To eliminate one variable, we can make the coefficients of \( X \) equal. We can do this by multiplying the second equation by 2:
- The first equation remains: \( 12X + 8Y = 16 \)
- The second equation becomes: \( 12X + 20Y = 22 \)

### Step 5: Subtract the Equations
Now, we subtract the first equation from the second:
\[ (12X + 20Y) - (12X + 8Y) = 22 - 16 \]
This simplifies to:
\[ 12Y = 6 \]
Dividing both sides by 12 gives:
\[ Y = \frac{1}{2} \]
Thus, the cost of one Easy-Write pencil is \( Y = 0.50 \) dollars.

### Step 6: Substitute Back to Find \( X \)
Now we will substitute \( Y \) back into one of the original equations to find \( X \). We can use the second equation:
\[ 6X + 10Y = 11 \]
Substituting \( Y = \frac{1}{2} \):
\[ 6X + 10 \left(\frac{1}{2}\right) = 11 \]
This simplifies to:
\[ 6X + 5 = 11 \]
Subtracting 5 from both sides gives:
\[ 6X = 6 \]
Dividing by 6 gives:
\[ X = 1 \]
Thus, the cost of one Smooth-Glide pen is \( X = 1.00 \) dollars.

### Step 7: Calculate the Cost of 9 Pens and 9 Pencils
Now we need to find the cost of 9 Smooth-Glide pens and 9 Easy-Write pencils:
\[ 9X + 9Y = 9(1) + 9\left(\frac{1}{2}\right) \]
Calculating this gives:
\[ 9 + \frac{9}{2} = 9 + 4.5 = 13.5 \]
Thus, the total cost of 9 Smooth-Glide pens and 9 Easy-Write pencils is \( 13.5 \) dollars.

### Final Answer
The cost of 9 Smooth-Glide pens and 9 Easy-Write pencils is **13.5**.

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