Question
A bicycle shop offers a 30% discount on all bicycles. David spent 25% of his savings on a
discounted mountain bike. He paid $210 for the bike after the discount.
A) How much money did David have in his savings account before buying the bike?
B)David wants to use the rest of the money in his savings account to buy a bike helmet
that originally costs $80.Does David have enough money left to buy the helmet?
c) David’s cousin works at the bike shop and gets an additional 15% off the already
discounted price.If David’s cousin buys the helmet for him, how much will the cousin
pay?
discounted mountain bike. He paid $210 for the bike after the discount.
A) How much money did David have in his savings account before buying the bike?
B)David wants to use the rest of the money in his savings account to buy a bike helmet
that originally costs $80.Does David have enough money left to buy the helmet?
c) David’s cousin works at the bike shop and gets an additional 15% off the already
discounted price.If David’s cousin buys the helmet for him, how much will the cousin
pay?
Answers
GPT-4o mini
To solve the problem, let's break it down step by step.
### A) How much money did David have in his savings account before buying the bike?
1. David paid $210 for the mountain bike after a 30% discount. Let's calculate the original price of the bike before the discount:
- Let \( P \) be the original price of the mountain bike.
- The bike is sold at a 30% discount, which means David paid 70% of the original price.
- Therefore, we have:
\[
0.7P = 210
\]
- Solving for \( P \):
\[
P = \frac{210}{0.7} = 300
\]
2. David spent 25% of his savings on this discounted bike. Let \( S \) be the total amount of money he had in his savings account. The amount he spent on the bike can then be expressed as:
\[
0.25S = 210
\]
- Solving for \( S \):
\[
S = \frac{210}{0.25} = 840
\]
**Answer for A:** David had $840 in his savings account before buying the bike.
### B) Does David have enough money left to buy the helmet?
1. After buying the bike, David spent \( 25\% \) of his savings, so the remaining amount in his savings after the purchase is:
\[
\text{Remaining Savings} = S - 210 = 840 - 210 = 630
\]
2. The cost of the bike helmet is $80. We check if David has enough money:
\[
630 \geq 80
\]
- Since \( 630 \) is greater than \( 80 \), David does have enough money left to buy the helmet.
**Answer for B:** Yes, David has enough money left to buy the helmet.
### C) How much will David’s cousin pay for the helmet?
1. David's cousin gets an additional 15% off the original price of the helmet, which is $80. First, calculate the additional discount:
- The amount of discount is:
\[
\text{Discount} = 0.15 \times 80 = 12
\]
2. The price after the discount is then:
\[
\text{Price after discount} = 80 - 12 = 68
\]
**Answer for C:** David’s cousin will pay $68 for the helmet.
### A) How much money did David have in his savings account before buying the bike?
1. David paid $210 for the mountain bike after a 30% discount. Let's calculate the original price of the bike before the discount:
- Let \( P \) be the original price of the mountain bike.
- The bike is sold at a 30% discount, which means David paid 70% of the original price.
- Therefore, we have:
\[
0.7P = 210
\]
- Solving for \( P \):
\[
P = \frac{210}{0.7} = 300
\]
2. David spent 25% of his savings on this discounted bike. Let \( S \) be the total amount of money he had in his savings account. The amount he spent on the bike can then be expressed as:
\[
0.25S = 210
\]
- Solving for \( S \):
\[
S = \frac{210}{0.25} = 840
\]
**Answer for A:** David had $840 in his savings account before buying the bike.
### B) Does David have enough money left to buy the helmet?
1. After buying the bike, David spent \( 25\% \) of his savings, so the remaining amount in his savings after the purchase is:
\[
\text{Remaining Savings} = S - 210 = 840 - 210 = 630
\]
2. The cost of the bike helmet is $80. We check if David has enough money:
\[
630 \geq 80
\]
- Since \( 630 \) is greater than \( 80 \), David does have enough money left to buy the helmet.
**Answer for B:** Yes, David has enough money left to buy the helmet.
### C) How much will David’s cousin pay for the helmet?
1. David's cousin gets an additional 15% off the original price of the helmet, which is $80. First, calculate the additional discount:
- The amount of discount is:
\[
\text{Discount} = 0.15 \times 80 = 12
\]
2. The price after the discount is then:
\[
\text{Price after discount} = 80 - 12 = 68
\]
**Answer for C:** David’s cousin will pay $68 for the helmet.