A storeowner mixed 8 pounds of peanuts and 5 pounds of M&M's. This 13 pound mixture sold for $55.27. A second mixture included 6 pounds of peanuts and 4 pounds of M&M's. This 10 pound mixture sold for $42.70. Find the cost per pound of the peanuts and M&M's.

Suppose a pound of peanuts is priced at X, M&M is Y, and the equation is 6X+4Y=42.70 8X+5Y=55.27. [8X+5Y=55.27]4-[6X+4Y=42.70]5 is [32X+20Y=221.08] - [30X+20Y=213.5] X=3.79 Y=4.99

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kobenhavn kobenhavn · Answer 2 · 2021-10-02T02:41:44-04:00

The cost per pound of the peanuts is $@@MATH_TOKEN_0@@ and M&M's is $$9.326$.

Let the cost per pound of the peanuts be $ @@MATH_TOKEN_2@@.

And, the cost per pound of the M&M's be $ $y$.

$8x+5y=55.27...(i)$

$5x+4y=42.70...(ii)$

Multiply $(i)$ by $4$ and $(ii)$ by $5$,

$32x+20y=221.08...(iii)$

$25x+20y=213.5...(iv)$

Subtract $(ii)$ from $(i)$,

$32x-25x+20y-20y=221.08-213.5$

$7x=7.58$

$x=1.08$

Substitute this value in $(i)$,

$8x+5y=55.27$

$8(1.08)+5y=55.27$

$8.64+5y=55.27$

$5y=55.27-8.64$

$5y=46.63$

$y=9.326$

So, the cost per pound of the peanuts is $@@MATH_TOKEN_24@@ and M&M's is $$9.326$.

Learn more about substitution method here:

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