SOLUTION: A gift basket contains jars of jam and bread mix that costs $45. There are 8 items in the basket. Jam costs $6 and bread mix costs $5. Write and solve linear equations to find the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A gift basket contains jars of jam and bread mix that costs $45. There are 8 items in the basket. Jam costs $6 and bread mix costs $5. Write and solve linear equations to find the       Log On


   

Question 1069635: A gift basket contains jars of jam and bread mix that costs $45. There are 8 items in the basket. Jam costs $6 and bread mix costs $5. Write and solve linear equations to find the jars of jam and packs of bread mix in the basket. Let x = jars of jam, and y = packs of bread mix
What are the system of equations?
There are how many jars of jam?
There are how many packs of bread mix?
I am lost after putting together the 1st equation 6x+5y=45 is the other x+y=8??? Please help
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
No reason to be lost. The equations appear good.

Account for how many items in the basket:
x%2By=8

Account for the resulting basket price:
6x%2B5y=45
-
Look at the units.
6%28dollars%2Fjam%29%2Ax%28jam%29%2B5%28dollars%2Fbread%29%2Ay%28bread%29=dollars
So no trouble in the units.


The system should be plainly obvious:
system%28x%2By=8%2C6x%2B5y=45%29

Find the intersection of the two lines. Same as find the x and y combination that satisfies both equations. Substitution Method, if that is the only way you know; or Elimination Method, if you prefer it.


--
Multiply first equation by 5, revise system:
system%285x%2B5y=40%2C6x%2B5y=45%29

Subtract first from second:
highlight%28x=5%29
-
Return to simpler item count equation, x%2By=8.
Find y.
y=8-x
y=8-5
highlight%28y=3%29


RESULT:
x=5 jars of jam
and
y=3 bread-mixes