Answer:
1 medal
5 trophies
Step-by-step explanation:
Use information from the question to <u>write equations</u> 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 <u>substitution method</u>.
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.
