Question

Four tomatoes and eight avocados cost $10. Six tomatoes and fourteen avocados cost $17.

Answer 1

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:

$4T + 8A = 10$ --- (1)

$6T + 14A = 17$ --- (2)

Solving (a): The price of each

Multiply (1) by 1.5

$1.5(4T + 8A = 10)$

$6T + 12A = 15$ --- (3)

Subtract (3) from (2)

$(6T + 14A = 17) - (6T + 12A = 15)$

$6T - 6T + 14A - 12A = 17 - 15$

$14A - 12A = 17 - 15$

$2A = 2$

Divide both sides by 2

$A = 1$

Substitute 1 for A in (1)

$4T + 8A = 10$

$4T + 8(1) = 10$

$4T + 8 = 10$

Make 4T the subject

$4T = 10 - 8$

$4T = 2$

Divide both sides by 4

$T = \frac{2}{4}$

$T = 0.5$

Solving (b): Analysis

In (a), we have:

$T = 0.5$

$A = 1$

We can say that an avocado costs twice as much as a tomato