How many of does he have?

Question

Mason has a collection of 49 cent stamps,20 cent stamps,and 3 cent stamps worth $23.55.He has 56 total 49 cent and 20 cent stamp and the number of 3 cent stamps is nine more than the number of 20 cent stamps.

Answer 1

Olivia:

Let’s expand on Mark’s response for the equation setup (using the revised 3¢ stamp cost)…..

0.20x + 0.03(x+9) + 0.49(56–x) = 23.55…..from given info

0.20x + 0.03x + 0.27 + 27.44 - 0.49x = 23.55….distribution property

-0.26x + 27.53 = 23.55….combine like terms

-0.26x = -4.16..…subtract 27.53 from

both sides of

equation

0.26x = 4.16……multiply both sides

of equation by (-1)

x = 16………divide both sides

by 0.26

Let’s check our answer by substituting x =16 back into our

original equation….

0.20(16) + 0.03(16+9) + 0.49(56-16) = 23.55

3.20 + 0.03(25) +0.49(40) = 23.55

3.20 + 0.75 + 19.60 = 23.55

23.55 = 23.55 True √, our answer

is correct. Always

check your work!

So Mason has…

25 - 3¢ stamps for $0.75

16 - 20¢ stamps for $3.20

40 - 49¢ stamps for $19.60…all totaling $23.55



Tip…to avoid math calculations involving decimals, we could multiply every term in our original equation by 100 to start and get…..20x + 3(x+9) + 49(56-x) = 2355. Try solving this equation for “x” using the same steps above. You should arrive at x=16 again.

Answer 2

x represents the number of 20¢ stamps

x + 3 represents the number of 3¢ stamps

56 - x represents the number of 49¢ stamps

0.20x + 0.03(x + 3) + 0.49(56 - x) = 23.55

Can you solve for x and answer?