SOLUTION: I need help on this problem: At a grocery store, a customer pays a total of $11.10 for 1.6 pounds of chicken and 2 pounds of fish. Another customer pays a total of $12.15 for 2.

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Question 137791: I need help on this problem:
At a grocery store, a customer pays a total of $11.10 for 1.6 pounds of chicken and 2 pounds of fish. Another customer pays a total of $12.15 for 2.4 pounds of chicken and 1.8 pounds of fish. How much do 2 pounds of chicken and 2 pounds of fish cost. Explain
Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
a grocery store, a customer pays a total of $11.10 for 1.6 pounds of chicken and 2 pounds of fish. Another customer pays a total of $12.15 for 2.4 pounds of chicken and 1.8 pounds of fish. How much do 2 pounds of chicken and 2 pounds of fish cost. Explain
:
Let x = price per pound for chicken
Let y = price per pound for fish
:
Write an equation for each statement:
:
"customer pays a total of $11.10 for 1.6 pounds of chicken and 2 pounds of fish."
1.6x + 2y = 11.10
2y = 11.10 - 1.6x
:
Divide equation by 2:
y = (5.55 - .8x); use this for substitution
:
"customer pays a total of $12.15 for 2.4 pounds of chicken and 1.8 pounds of fish"
2.4x + 1.8y = 12.15
;
Substitute (5.55-.8x) for y in the above equation; solve for x:
2.4x + 1.8(5.55-.8x) = 12.15
;
2.4x + 9.99 - 1.44x = 12.15; multiply whats inside the brackets
:
2.4x - 1.44x = 12.15 - 9.99
:
.96x = 2.16
x =
x = $2.25 a lb for chicken; 2 lbs = $5.50
:
Find y using the 1st equation:
1.6(2.25) + 2y = 11.10
:
3.6 + 2y = 11.10
:
2y = 11.10 - 3.6
:
2y = 7.5
y =
y = $3.75 a lb for fish; 2 lbs = $7.50
:
How much do 2 pounds of chicken and 2 pounds of fish cost.
5.50 + 7.50 = $13.00
:
:
Check solutions using the 2nd equation:
2.4(2.25) + 1.8(3.75) =
5.40 + 6.75 = 12.15;