3 pounds of squash and 2 pounds of eggplant cost $2.85. The cost of 4 pounds of squash and 5 pounds of eggplant is $5.41. What is the cost of each pound?
3p + 2e = $2.85
4p + 5p = $5.41
Answer? .58 cents a pound
3p + 2e = $2.85
4p + 5e = $5.41
Multiply top equation by 5 and bottom by 2.
15p + 10e = 14.25
8p + 10e = 10.82
Subtract bottom equation from top and solve for p. Then use top original equation to solve for e. Insert both values into bottom original equation to check answers.
To solve this problem, we can set up a system of equations using the given information. Let p represent the cost per pound of squash and e represent the cost per pound of eggplant.
From the first statement, we can write the equation:
3p + 2e = $2.85
From the second statement, we can write the equation:
4p + 5e = $5.41
Now, we can solve this system of equations to find the values of p and e.
One way to solve this system of equations is by using the method of substitution or elimination. However, since this is a simple problem and the calculations are not too complex, we can use the substitution method.
From the first equation, we can solve for p in terms of e by subtracting 2e from both sides:
3p = $2.85 - 2e
Now, we can substitute this expression for p into the second equation:
4($2.85 - 2e) + 5e = $5.41
Distribute the 4 to the terms inside the parentheses:
11.4 - 8e + 5e = $5.41
Combine like terms:
-3e + 11.4 = $5.41
Subtract 11.4 from both sides:
-3e = $5.41 - $11.4
-3e = -$5.99
Divide both sides by -3 to solve for e:
e = -$5.99 / -3
e = $1.9967 (approximately)
Now that we have the cost per pound of eggplant, we can substitute this value back into the first equation to solve for p:
3p + 2($1.9967) = $2.85
3p + $3.9934 = $2.85
3p = $2.85 - $3.9934
3p = -$1.1434
Dividing both sides by 3:
p = -$1.1434 / 3
p = $0.3811 (approximately)
Therefore, the cost per pound of squash (p) is approximately $0.3811 and the cost per pound of eggplant (e) is approximately $1.9967.