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[Smart Math] Algebra Problem 14

Here’s and example of a SMART MATH problem for ALGEBRA.

Problem

8 mangoes and 6 apples can be purchased for \$9.60 and 6 mangoes and 8 apples for \$10. How much does each apple cost?

1. 50p
2. 60p
3. 70p
4. 80p
5. 90p

The Usual Method

Let the cost of 1 mango be ‘m’ cents and one apple be ‘n’ cents.

Hence  8m + 6n = 960                         ..…. Eq. 1.

And     6m + 8n = 1000                       ..…. Eq. 2.

Solving both these equations simultaneously as follows:

Multiplying Eq. 1 with 6 and Eq. 2 with 8, we get:

48m + 36n = 5760                   ..…. Eq. 3.

And     48m + 64n = 8000                   ..…. Eq. 4.

Subtraction Eq. 3 from Eq. 4, we get:

28n = 2240

$\therefore$n = 80p

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

Let the cost of 1 mango be ‘m’ cents and one apple be ‘n’ cents.

Hence  8m + 6n = 960                         ..…. Eq. 1.

And     6m + 8n = 1000                       ..…. Eq. 2.

Subtraction Eq. 1 from Eq. 2, we get:

2m + 2n = 40

$\therefore$m + n = 20

This means that the price of the apple is 20 p more than that of a mango.

Assuming that m = n (i.e. the price of mango = price of apple)

$\therefore$6m + 8n = 1000 becomes 6n + 8n = 1000

$\therefore$14n = 1000

$\therefore n\approx 70$p

Now since n > m by 20p, n > average of n and m by 10p.

$\therefore n\approx 70+10=80$p

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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