Asked by Optional
Marlita made paper crane mobiles for her teachers on teachers day. She spent 50% of the money in her savings on coloured papers and 20% of the remainder on coloured thread. She then had $8 left. How much money did she spend on the materials?
Answers
Answered by
GPT-4o mini
Let \( x \) be the total amount of money Marlita had in her savings.
1. Marlita spent 50% of her money on colored papers:
\[
\text{Amount spent on colored papers} = 0.5x
\]
After this purchase, the remaining money is:
\[
\text{Remaining money} = x - 0.5x = 0.5x
\]
2. Next, Marlita spent 20% of the remaining money on colored thread:
\[
\text{Amount spent on colored thread} = 0.2 \cdot 0.5x = 0.1x
\]
After this purchase, the remaining money is:
\[
\text{Remaining money} = 0.5x - 0.1x = 0.4x
\]
3. We know that this remaining money is $8:
\[
0.4x = 8
\]
4. We can solve for \( x \):
\[
x = \frac{8}{0.4} = 20
\]
Thus, Marlita initially had $20. Now we can calculate how much she spent on materials:
- Amount spent on colored papers:
\[
0.5x = 0.5 \times 20 = 10
\]
- Amount spent on colored thread:
\[
0.1x = 0.1 \times 20 = 2
\]
5. Total amount spent on materials:
\[
\text{Total spent} = \text{Amount spent on papers} + \text{Amount spent on thread} = 10 + 2 = 12
\]
Therefore, Marlita spent a total of \(\boxed{12}\) dollars on materials.
1. Marlita spent 50% of her money on colored papers:
\[
\text{Amount spent on colored papers} = 0.5x
\]
After this purchase, the remaining money is:
\[
\text{Remaining money} = x - 0.5x = 0.5x
\]
2. Next, Marlita spent 20% of the remaining money on colored thread:
\[
\text{Amount spent on colored thread} = 0.2 \cdot 0.5x = 0.1x
\]
After this purchase, the remaining money is:
\[
\text{Remaining money} = 0.5x - 0.1x = 0.4x
\]
3. We know that this remaining money is $8:
\[
0.4x = 8
\]
4. We can solve for \( x \):
\[
x = \frac{8}{0.4} = 20
\]
Thus, Marlita initially had $20. Now we can calculate how much she spent on materials:
- Amount spent on colored papers:
\[
0.5x = 0.5 \times 20 = 10
\]
- Amount spent on colored thread:
\[
0.1x = 0.1 \times 20 = 2
\]
5. Total amount spent on materials:
\[
\text{Total spent} = \text{Amount spent on papers} + \text{Amount spent on thread} = 10 + 2 = 12
\]
Therefore, Marlita spent a total of \(\boxed{12}\) dollars on materials.
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