Final answer:
By solving two simultaneous equations, we found that 1 apple costs $0.15 and 1 banana costs $0.23. Adding these together, the total cost of 1 apple and 1 banana is $0.38, which rounds up to the closest given option of $0.39.
Step-by-step explanation:
To find the total cost of 1 apple and 1 banana, we can set up two equations based on the given information:
- 3 apples + 4 bananas = $1.37 (equation 1)
- 5 apples + 7 bananas = $2.36 (equation 2)
We can solve these equations simultaneously to determine the cost of each individual fruit. Multiplying equation 1 by 5 and equation 2 by 3 gives us:
- 15 apples + 20 bananas = $6.85 (equation 3)
- 15 apples + 21 bananas = $7.08 (equation 4)
We subtract equation 3 from equation 4 to find the cost of one banana:
- 1 banana = $7.08 - $6.85
- 1 banana = $0.23
Plugging the cost of 1 banana back into equation 1, we can find the cost of 1 apple:
- 3 apples + 4($0.23) = $1.37
- 3 apples + $0.92 = $1.37
- 3 apples = $1.37 - $0.92
- 3 apples = $0.45
- 1 apple = $0.45 / 3
- 1 apple = $0.15
Adding the costs of 1 apple and 1 banana gives the total cost:
- 1 apple + 1 banana = $0.15 + $0.23
- 1 apple + 1 banana = $0.38
Therefore, the closest answer to the options given is $0.39, which is option a.