Question

Melissa buys 2 1/2 pounds of salmon and 1 1/4 pounds of swordfish. She pays a total of $31.25, and the swordfish cost $.20 per pound less than the salmon. What would be the combined cost of 1 pound of salmon and 1 pound of swordfish

Answer 1

Answer:

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.66

Step-by-step explanation:

Let us assume the cost of 1 pound salmon = $ m

So the cost of 1 pound of 1 pound swordfish cat = $ ( m - 0.20)

Now, the Amount of salmon purchased  = 2 1/2 pounds

$2\frac{1}{2} = 2 + \frac{1}{2} = 2 + 0.5 = 2.5$

So, the amount of salmon purchased = 2.5 pounds

Cost of buying 2.5 pounds = 2.5 x ( 1 pound cost)

= 2.5 ( m) = $ 2.5 m  ...... (1)

Also, the Amount of swordfish purchased  = 1 1/4 pounds

$1\frac{1}{4} = 1 + \frac{1}{4} = 1 + 0.25 = 1.25$

So, the amount of swordfish purchased = 1.25 pounds

Cost of buying 1.25 pounds = 1.25 x ( 1 pound cost of swordfish)

= 1.25 ( m - 0.20) = $ 1.25 m - 0.25       .... (2)

Now, the combined cost paid  = $ 31.25

⇒Cost of buying (2.5 pounds salmon  +  1.25 pounds swordfish) = $ 31.25

or, 2.5 m +   1.25 m - 0.25  = 31.35       (from (1) and (2))

or, 3.75 m = 31.60

or, m = 31.60/3.75 =  8.43

⇒ m = $8.43

So, the cost of 1 pound salmon = m = $8.43

and the cost of 1 pound swordfish = m - 0.20 = $8.43 - 0.20 = $ 8.23

Hence, the combined cost  1 pound of salmon and 1 pound of swordfish = $8.43 + $ 8.23 =  $ 16.66