Certainly! Let's solve this problem step-by-step:
1. Identify the costs and ratio:
- The cost to print one black and white page is £0.10 (10p).
- The cost to print one color page is £0.15 (15p).
- The ratio of black and white pages to color pages is 4:1.
2. Express the quantities in terms of a single variable:
- Let the number of color pages be [tex]\( x \)[/tex].
- Since the ratio of black and white pages to color pages is 4:1, the number of black and white pages will be [tex]\( 4x \)[/tex].
3. Set up the equation for the total cost:
- The total cost to print all pages is £5.50.
- The cost to print [tex]\( 4x \)[/tex] black and white pages is [tex]\( 4x \times 0.10 \)[/tex] pounds.
- The cost to print [tex]\( x \)[/tex] color pages is [tex]\( x \times 0.15 \)[/tex] pounds.
- The total cost equation will be:
[tex]\[
4x \times 0.10 + x \times 0.15 = 5.50
\][/tex]
4. Simplify and solve the equation:
- Simplify the left side of the equation:
[tex]\[
0.40x + 0.15x = 5.50
\][/tex]
- Combine the terms:
[tex]\[
0.55x = 5.50
\][/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.50}{0.55} = 10
\][/tex]
Therefore, [tex]\( x = 10 \)[/tex]. This means there are 10 color pages.
5. Calculate the number of black and white pages:
- Since the number of black and white pages is [tex]\( 4x \)[/tex]:
[tex]\[
4x = 4 \times 10 = 40
\][/tex]
Therefore, there are 40 black and white pages.
6. Calculate the total number of pages printed:
- Total pages = black and white pages + color pages:
[tex]\[
40 + 10 = 50
\][/tex]
So, Mrs. Henderson prints 50 pages in total: 40 black and white pages and 10 color pages.
