Question

Daniel goes to a store and buys 4 lbs of peanuts and 5 lbs of almonds for $44. Josh goes to the same store and buys 2 lbs of peanuts and 4 lbs of almonds for $31. What is the cost of 1 pound of peanuts?

Answer 1

Step-by-step explanation:

Aloha !

Let a be peanuts and b be almonds .

Now,

4a+5b=44--->1×1

2a+4b=31---->2×2

Solving 1 and 2,

4a+5b=44

4a+8b=62

-_________

-3b=18

b= - 18/3

b=-6

Now, replacing in any equation .

2a+4b=31

2a+4(-6)=31

2a-24=31

2a=55

a=55/2

a=22.5

Verification :-

2(55/2)+4(-6)=31

55-24=31

31=31

Thank you

@ Twilight Astro ✌️☺️♥️

Answer 2

$\huge{\bold{ Solution:-}}$

$Let \: the \: cost \: of \: peanuts \: be \: x \: and \: \\ cost \: of \: almonds \: be \: y. \\ \\ {\red{\small{{\mathbb{According \: to \: question:-}}}}} \\ \\ 4x + 5y = 44 - (1) \\ \\ 2x + 4y = 31 - (2) \\ \\ multiply \: by \: 2 \: in \: equ. \: (2) = \\ \\ 4x + 8y = 62 - (3) \\ \\ subtracting \: equ \: (2) \: and \: (3) = \\ \\ 4x + 5y - (4x + 8y) = 44 - 62 \\ \\ 4x + 5y - 4x - 8y = - 18 \\ \\ - 3y = - 18 \\ \\ y = \frac{18}{3} \\ \\ \small{\blue{\underline{\purple{\mathbb{y = 6}}}}} \\ \\ putting \: y = 6 \: in \: equ. \: (1) \\ \\ 4x + 5y = 44 \\ \\ 4x + 5 \times 6 = 44 \\ \\ 4x + 30 = 44 \\ \\ 4x = 44 - 30 \\ \\ 4x = 14 \\ \\ x = \frac{14}{4} \\ \\ \small{\blue{\underline{\purple{\mathbb{x = \frac{7}{2} }}}}} \\ \\ x = 3.5 \\ \\ Therefore, \: the \: cost \: of \: peanuts \: is \: \: 3.5 \\ \\ \small{\red{\underline{\purple{\mathbb{Verification}}}}} \\ \\ putting \: x \: and \: y \: in \: equ \: (1) = \\ \\ 4x + 5y = 44 \\ \\ LHS = \\ = 4 \times \frac{7}{2} + 5 \times 6 \\ \\ = 14 + 30 \\ \\ = 44 = RHS \\ \\ Verified$

Hope its helpful ❤