How would I work this word problem out?

The math club and the science club had fundraisers to buy supplies for a hospice. The math club spent 135$ buying 6 cases of juice and one case of bottled water. The science club spent 110$ buying 4 cases of juice and 2 cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost?





How would I work this out? (It involves linear equations)How would I work this word problem out?
let J be the cost of one case of juice and W be the cost of a bottled water





if so, then we could say:


6J + W = 135; and


4J + 2W = 110





then we can solve for J and W!





solving for J first:


2(6J + W = 135)


-(4J + 2W = 110)


-----------------------


8J = 160


J = $20





solving for W:


6J + W = 135


6(20) + W = 135


W = 135 - 120


W = $15





check:


6J + W = 135


6(20) + 15 = 135 --%26gt;%26gt; correct!





4J + 2W = 110


4(20) + 2(15) = 110 --%26gt;%26gt; correct!














ciao!!How would I work this word problem out?
the first thing you do is set up equations for the two sets of informatio.





let x = cases of juice and let y = cases of bottled water





135 = 6x + 1y


and


110 = 4x + 2y





you can reorganise these two equations however you would like but for times sake lets do the first equation. it changes to: 135 - 6x = y you then substitute that equation into the second at ';y'; and solve for ';x';. from there you can put the ';x'; value in and solve for ';y'; in either equation. and there is your answer.