Answer:
(a)
A single avocado costs $1
A single tomato costs $0.5
(b)
An avocado costs twice as much as a tomato
Step-by-step explanation:
Represent the tomatoes with T and the avocados with A.
So, we have:
[tex]4T + 8A = 10[/tex] --- (1)
[tex]6T + 14A = 17[/tex] --- (2)
Solving (a): The price of each
Multiply (1) by 1.5
[tex]1.5(4T + 8A = 10)[/tex]
[tex]6T + 12A = 15[/tex] --- (3)
Subtract (3) from (2)
[tex](6T + 14A = 17) - (6T + 12A = 15)[/tex]
[tex]6T - 6T + 14A - 12A = 17 - 15[/tex]
[tex]14A - 12A = 17 - 15[/tex]
[tex]2A = 2[/tex]
Divide both sides by 2
[tex]A = 1[/tex]
Substitute 1 for A in (1)
[tex]4T + 8A = 10[/tex]
[tex]4T + 8(1) = 10[/tex]
[tex]4T + 8 = 10[/tex]
Make 4T the subject
[tex]4T = 10 - 8[/tex]
[tex]4T = 2[/tex]
Divide both sides by 4
[tex]T = \frac{2}{4}[/tex]
[tex]T = 0.5[/tex]
Solving (b): Analysis
In (a), we have:
[tex]T = 0.5[/tex]
[tex]A = 1[/tex]
We can say that an avocado costs twice as much as a tomato
