A confectionery sells strawberry sandwiches and apricot sandwiches.

Strawberry sandwiches	Apricot sandwiches
6 for $2.30	5 for $3.40

Shiyun bought an equal number of strawberry sandwiches and apricot sandwiches. She paid $53.40 more for the apricot sandwiches and the strawberry sandwiches.

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

(a)
Shiyun bought an equal number of strawberry sandwiches and apricot sandwiches.  Make the number of strawberry sandwiches and apricot sandwiches the same.  LCM of 6 and 5 is 30.

Number of sets of 6 in 30
= 30 ÷ 6
= 5

Cost of 1 set of 30 strawberry sandwiches
= 5 x 2.30
= $11.50

Number of sets of 5 in 30
= 30 ÷ 5
= 6

Cost of 1 set of 30 apricot sandwiches
= 6 x 3.40
= $20.40

Amount that Shiyun paid more for 1 set of 30 apricot sandwiches than 1 set of 30 strawberry sandwiches
= 20.40 - 11.50
= $8.90

Number of sets of $8.90
= 53.40 ÷ 8.90
= 6

Total number of sandwiches in 1 set of 30 apricot sandwiches and 30 strawberry sandwiches
= 2 x 30
= 60

Number of sandwiches that Shiyun bought
= 6 x 60
= 360

(b)
Cost of sandwiches in 1 set of 30 apricot sandwiches and 30 strawberry sandwiches
= 11.50 + 20.40
= $31.90

Total amount that Shiyun spent altogether
= 6 x 31.90
= $191.40

Answer(s): (a) 360 ; (b) $191.40