After the school opening announcement, Salem plans to set a new selling price for all items in his shop. His current stock has a lot of stationery sets, few shoes and few school uniforms. Let's assume that several of his customers; Abu bought 3 stationery sets and 2 pairs of shoes for RM100 and Amirul bought 5 stationery sets and a pair of shoes for RM78.
a. Write simultaneous equations for the above situation.
b. With the substitution method, determine the new selling price for shoes.
c. With the elimination method, find the new selling price for stationery sets.
a. Let x be the selling price of stationery sets and y be the selling price of shoes.
From the information given, we can create two equations:
3x + 2y = 100
5x + y = 78
b. Using the substitution method:
From the second equation, y = 78 - 5x
Substitute this into the first equation:
3x + 2(78 - 5x) = 100
3x + 156 - 10x = 100
-7x = -56
x = 8
Therefore, the new selling price for shoes is RM8.
c. Using the elimination method:
Multiply the first equation by 5 and the second equation by 3 to eliminate y:
15x + 10y = 500
15x + 3y = 234
Subtract the second equation from the first:
7y = 266
y = 38
Therefore, the new selling price for stationery sets is RM38.