A gift basket that contains jars of jam and packages of bread mix costs $45. there are 8 items in the basket. jars of jam cost $
6 each, and packages of bread mix cost $5 each. write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix in the gift basket. let x represent the number of jars of jam and let y represent the number of packages of bread mix.system of equations:
------------------------------------------------------ Define jam and bread mix ------------------------------------------------------ Let the number of jar of jam be x Let the number of packages of bread mix be y
------------------------------------------------------ Form equations and solve ------------------------------------------------------ x + y = 8 --------------------- (1) 6x + 5y = 45 ---------------- (2)
------------------------------------------------------ Rewrite equation to make x the subject ------------------------------------------------------ x+ y = 8 x = 8 - y ----------------------------(1a)
------------------------------------------------------ Substitute (1a) into (2) ------------------------------------------------------ 6(8 - y) + 5y = 45 48 - 6y + 5y = 45 y = 48 - 45 y = 3
------------------------------------------------------ Substitute y = 3 into (1) to find x ------------------------------------------------------ x + 3 = 8 x = 8 - 3 x = 5
------------------------------------------------------ Find jam and bread mix ------------------------------------------------------ Jars of Jam = x = 5 Packages of bread mix = y = 3
