Raj has $10. if he buys 8 pears and 5 mangoes, he will be short of $1.10. if he buys 5 pears and 4 mangoes , he will receive $1.75 in change. find the price of 1 pear and 1 mango.

1 pear = $0.45

1 mango = 1.5

Step-by-step explanation:

8 pears + 5 mangoes = $11.10 ➡ 8p + 5m = 11.10

5 pears + 4 mangoes = $8.25 ➡ 5p + 4m = 8.25

multiply first equation by -4 and second one by 5

-4 ×(8p+5m) = 11.10 ➡ -32p - 20m = 44.4

5 ×(5p+4m) = 8.25 ➡ 25p + 20m = 41.25

add both equations up

-32p - 20m + 25p + 20m = 44.4 + 41.25

-7p = 3.15 ➡ p = $0.45

use this value to find the price of mango

5×0.45 + 4×m = 8.25 ➡ 2.25 + 4m = 8.25 ➡ 4m = 6 ➡ m = $1.5