you have a total of six trophies and medals to give as prizes for a contest. a trophy cost $12 and a metal cost three dollars. you spend a total of $63 how many of each item did you buy?

1 medal

5 trophies

Step-by-step explanation:

Use information from the question to write equations algebraically.

let 't' be the number of trophies

let 'm' be the number of medals

Equation for cost of prizes

12t + 3m = 63 "trophy cost $12 and a metal cost three dollars. you spend a total of $63"

Equation for total prizes

t + m = 6 "you have a total of six trophies and medals"

Solve using substitution method.

Rearrange the equation for total prizes to isolate "t". Subtract "m" from each side. It will cancel out on the left.

t = 6 - m

Use the new equation and substitute "t" for 6-m into 12t + 3m = 63.

12t + 3m = 63

12 (6-m) + 3m = 63 Distribute over brackets

72 - 12m + 3m = 63 Combine like terms (-12m+3m)

72 - 9m = 63 Start isolating "m"

72 - 72 - 9m = 63 - 72 Subtract 72 from both sides

-9m = 63 - 72 72-72 cancelled out on the left.

-9m = - 9

-9m/-9 = - 9/-9 Divide both sides by - 9 to isolate "m"

m = 1 Number of medals bought

Substitute what you found for "m" into any of the equations to find "t".

t = 6 - m

t = 6 - 1 Subtract

t = 5 Number of trophies bought

Therefore you bought 1 medal and 5 trophies.

You bought 5 trophies and one medal because 12x5=60 and 60+3=63 and that's 6total