Question

ten mangoes and twelve avocados cost $23. five mangoes and four avocados cost $10. how much do one mango and one avocado cost? $\square$

Explanation:

Step1: Define variables

Let $m$ = cost of 1 mango, $a$ = cost of 1 avocado.

Step2: Set up equations

$$10m + 12a = 23$$
$$5m + 4a = 10$$

Step3: Eliminate $m$ variable

Multiply the second equation by 2: $10m + 8a = 20$
Subtract from first equation:
$$(10m + 12a) - (10m + 8a) = 23 - 20$$
$$4a = 3$$
$$a = \frac{3}{4} = 0.75$$

Step4: Solve for $m$

Substitute $a=0.75$ into $5m + 4a = 10$:
$$5m + 4(0.75) = 10$$
$$5m + 3 = 10$$
$$5m = 7$$
$$m = \frac{7}{5} = 1.4$$

Step5: Find total for one of each

$$m + a = 1.4 + 0.75$$

Answer:

$\boldsymbol{2.15}$