A confectionery sells vanilla sandwiches and apple sandwiches.

Vanilla sandwiches	Apple sandwiches
6 for $2.80	4 for $4.60

Elyse bought an equal number of vanilla sandwiches and apple sandwiches. She paid $32.80 more for the apple sandwiches and the vanilla sandwiches.

1. How many sandwiches did she buy?
2. How much did she spend altogether?

(a)
Elyse bought an equal number of vanilla sandwiches and apple sandwiches.  Make the number of vanilla sandwiches and apple sandwiches the same.  LCM of 6 and 4 is 12.

Number of sets of 6 in 12
= 12 ÷ 6
= 2

Cost of 1 set of 12 vanilla sandwiches
= 2 x 2.80
= $5.60

Number of sets of 4 in 12
= 12 ÷ 4
= 3

Cost of 1 set of 12 apple sandwiches
= 3 x 4.60
= $13.80

Amount that Elyse paid more for 1 set of 12 apple sandwiches than 1 set of 12 vanilla sandwiches
= 13.80 - 5.60
= $8.20

Number of sets of $8.20
= 32.80 ÷ 8.20
= 4

Total number of sandwiches in 1 set of 12 apple sandwiches and 12 vanilla sandwiches
= 2 x 12
= 24

Number of sandwiches that Elyse bought
= 4 x 24
= 96

(b)
Cost of sandwiches in 1 set of 12 apple sandwiches and 12 vanilla sandwiches
= 5.60 + 13.80
= $19.40

Total amount that Elyse spent altogether
= 4 x 19.40
= $77.60

Answer(s): (a) 96 ; (b) $77.60