How many of each did he buy?

Question

Bob bought 22 stamps if the stamps were 22$ and some were 29$.And all in total he spent 540$ how many of each did he buy?

Answer 1

We have 2 unknowns so we need to have 2 equations to solve this problem.

Let x = number of $22 stamps he bought

y = number of $29 stamps he bought

Eq. I: x + y = 22

Eq. II: 22x +29y = 540

We can use either the substitution or the elimination method to solve this. Let's use the substitution method.

In Eq. I we can solve for x by subtracting y from both sides and getting x = 22 - y. Use this value for x in Eq. II and we can solve for y:

22x + 29y = 540 Eq. II

22(22-y) + 29y = 540 substituting for x

484 - 22y + 29y = 540 simplify

7y = 540 - 484 combine like terms

7y = 56 simplify

y = 56/7 divide both sides by 7 to isolate y

y = 8 solve for y

Using this value for y in Eq. I we can solve for x:

x = 22 - y Eq. I (re-arranged)

x = 22 - 8 substitute for y

x = 14 solve for x

Therefore, we see that Bob bought 14 $22 stamps and 8 $29 stamps.