Answer:
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.
