SOLUTION: My daughter needs help with this problem, she has a learning disability and these problems are very difficult for her and I can't help her either. Mama Mia owned a pizza shop. R

Question 276943: My daughter needs help with this problem, she has a learning disability and these problems are very difficult for her and I can't help her either.
Mama Mia owned a pizza shop. Recently she ordered 20 jars of canned tomato sauce and 25 pounds of cheese. The total was $170.50. The bill was not itemized so Mama Mia looked at past invoices. Last month she had ordered 25 jars of canned tomato sauce and 35 pounds of cheese. The total was $235. Using a system of equations, help Mama Mia determine the price of 1 jar of canned tomato sauce and 1 pound jar of cheese.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
These kind of problems seem to be hard for a lot of people.
Think and try to visualize what's happening here.
:
Recently she ordered 20 jars of canned tomato sauce and 25 pounds of cheese. The total was $170.50. The bill was not itemized so Mama Mia looked at past invoices. Last month she had ordered 25 jars of canned tomato sauce and 35 pounds of cheese. The total was $235. Using a system of equations, help Mama Mia determine the price of 1 jar of canned tomato sauce and 1 pound jar of cheese.
:
Let t = price of tomato sauce
Let c = price of cheese
:
write an equation each statement
:
" Recently she ordered 20 jars of canned tomato sauce and 25 pounds of cheese. The total was $170.50."
20t + 25c = 170.50
:
" Last month she had ordered 25 jars of canned tomato sauce and 35 pounds of cheese. The total was $235."
25t + 35c = 235
:
"Using a system of equations, " that just means there are two or more equations
:
"determine the price of 1 jar of canned tomato sauce and 1 pound jar of cheese."
:
We are going to use elimination here,
multiply each term in the 2nd equation by 4
multiply each term in the 1st equation by 5
Results:
100t + 140c = 940.00
100t + 125c = 852.50
---------------------Subtraction eliminates t, find c
0t + 15c = 87.50
c = ; divide both sides by 15
c = $5.83 for 1 lb of cheese
:
use the 1st equation to find t, substitute 5.83 for c
20t + 25c = 170.50
20t + 25(5.83) = 170.50
20t + 145.75 = 170.50
20t = 170.50 - 145.50
20t = 24.75
t =
t = $1.24 for a can of tomato sauce
:
:
Check our solutions in the 2nd equation
25t + 35c = 235
Substitute our solutions for t and c
25(1.24) + 35(5.83) = 235
31 + 204.50 = 235
235.50 ~ 235, a slight difference because we rounded the cents
:
How about this, did it shed some light? Questions? ankor@att.net

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