Multi step equation

Question

A bake sale was held at Juvena High to raise funds for an NGO. The sale of maple pecan pies amounted to 15 more than half the lemon tarts that were sold. The number of brownie pops sold amounted to two-thirds of the sale of maple pecan pies. If 223 pieces were sold in all, how many

lemon tarts were sold?

Answer 1

Good morning Jeff. Lets denote the number of maple pecan as MP, the number of lemon tarts as LT, and Brownie Pops as BP, then:

MP = 15 + LT/2

BP = 2/3 MP

and total sold = 223, thus we will have:

BP = (2/3)(15 + 1/2 LT),

so that total number sold = MP + BP + LT or:

223= 15 + (1/2)LT +(2/3)(15+(1/2}LT) + LT

or: (1/2)LT + (1/3)LT + LT = 223 - 15 - 10

which results in: 3LT + 2LT + 6LT = 198 or 11LT = 198 resulting in LT = 18;

Good Luck.

Answer 2

M = 15 + (1/2)L

B = (2/3)M

L + M + B = 223

L + [15 + (1/2)L] + (2/3)[15 + (1/2)L] = 223

L + 15 + (1/2)L + 10 + (1/3)L = 223

Clear fractions (multiply by 6)

6L + 90 + 3L + 60 + 2L = 1338

Collect terms

11L = 1188

Solve for L, then go back and get M first (from the 1st equation) and then

get B (from the 2nd equation).