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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

step-by-step explanation:

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