Question 1160938: A housewife purchases 5 liters of milk, 3 loaves of bread and 6 cans of tuna. She gives the cashier R200 and receives R54 change.
How much did all the items cost?
If a liter of milk costs R5 more than a can of tuna and a loaf of bread costs R2 less than a liter of milk, determine the cost of each item?
Found 3 solutions by Theo, josgarithmetic, saw:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! all the items cost 200 minus 54 = 146.
all of the money is in R$, so 146 means R146.
1 liter of milk costs 5 more than a can of tuna.
1 loaf of bread costs 2 less than a liter of milk.
the housewife purchases 5 liters of milk, 3 loaves of bread, and 6 cans of tuna.
let M equal the cost of a liter of milk.
let T equal the cost of a can of tuna.
let B equal the cost of a loaf of bread.
you get:
5M + 3B + 6T = 146.
a liter of milk costs 5 more than a can of tuna and a loaf of bread costs 2 less than a liter of milk, therefore:
M = T + 5.
B = M - 2.
from the first of these two equations, solve for T to get:
T = M - 5
the two equations become:
T = M - 5
B = M - 2
the equation of 5M + 3B + 6T = 146 becomes:
5M + 3(M-2) + 6(M-5) = 146
simplify to get:
5M + 3M - 6 + 6M - 30 = 146
combine like terms to get:
14M - 36 = 146
add 36 to both sides of the equation to get:
14M = 182
solve for M to get:
M = 182 / 14 = 13
since T = M - 5, then T = 8
since B = M - 2, then B = 11
your original equation is 5M + 3B + 6T = 146.
this becomes 5*13 + 3*11 + 6*8 = 146 which becomes 146 = 146, confirming the solution is correct.
your solution is:
the cost of a liter of milk is R13.
the cost of a loaf of bread is R11.
the cost of a can of tuna is R8.
Answer by josgarithmetic(39616)  (Show Source):
You can put this solution on YOUR website! Let the price for the TUNA be assigned the variable, p.
PRICE multiplied by QUANTITY is COST.
The description can be fit into this table:
PRICE QUANTITY COST
Milk p+5 5
Bread (p+5)-2 3
Tuna p 6
TOTAL 146
You should be able to fill other information, form an equation, and solve the problem.
Answer by saw(34) (Show Source):
You can put this solution on YOUR website! Let m = a liter of milk
Let b = a loaf of bread
Let t = a can of tuna
5m+3b+6t = R200-R54 = R146
If a liter of milk costs R5 more than a can of tuna
m = t+5
If a loaf of bread costs R2 less than a liter of milk
b = m-2
5m+3b+6t = 146
5(t+5)+3(m-2)+6t = 146
5t+25+3m-6+6t = 146
11t+3(t+5)+19 = 146
11t+3t+15+19 = 146
14t+34 = 146
14t = 112
t = 8
m = 13
b = 11
A liter of milk costs R13 and 5 liters of milk costs R65.
A loaf of bread costs R11 and 3 loaves of bread costs R33.
A can of tuna costs R8 and 6 cans of tuna costs R48.
Check-----
5m+3b+6t = R146
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