Answer:
Declan bought 3 books and 4 magazines
Step-by-step explanation:
Let number of books bought be x
Let number of magazines bought be y
Total number of books and magazines bought = x + y = 7
∴ x + y = 7 - - - - - (1)
x = 7 - y - - - - - (2)
we are also told that total amount spent = $33; when price per book = $5; and price per magazine = $4.5
∴ 5(x) + 4.5(y) = 33 - - - - - - - (3)
substituting equation 2 ( x = 7 - y ) into equation 3:
5(x) + 4.5(y) = 33
= 5 (7 - y) + 4.5(y) = 33
35 - 5y + 4.5y = 33
35 -0.5y = 33
35 = 33 + 0.5y
35 - 33 = 0.5y
0.5y = 2
y = 2 ÷ 0.5 = 4
∴ y = 4
solving for x, by putting the value of y into equation 2:
x = 7 - y - - - - (2)
x = 7 - 4 = 3
∴ x = 3
Therefore, Declan bought 3 books and 4 magazines.
