Explanation:
the 4 steps of a problem-solving plan :
1. understand and explore the problem.
2. find a strategy.
3. use the strategy to solve the problem.
4. look back and reflect on the solution.
1.
step 1 : aha, we have a ratio.
step 2 : that means we need to multiply both sides of the ratio by the same factor so that one side is showing the specified target number, and the other side gives us the result that still maintains the original ratio value.
step 3 :
2.14 out of 100 students play the trumpet.
the ratio is
2.14 / 100
there are 400 students.
400 = 4×100.
so, we need to multiply the ratio by 4/4.
2.14/100 × 4/4 = 8.56 / 400
step 4 :
rounded (as a fraction of a single person does not make any sense in this regard), about 9 students play the trumpet.
2.14 × 100 would give us a whole number of students (214). so, if we had 100×100 = 10000 students, we would not need to round : 214/10000. but simplifying this shows us that there is a smaller whole number solution :
107/5000 (107 out of 5000 students would play the trumpet).
2.
step 1 : this is a system of multiple equations with multiple variables.
step 2 : identify each equation and each variable. if there are not more variables than equations, solve the system.
step 3 :
T = distance by Tyrone = 79.25 m
B = distance by Brett
G = distance by Gabe
M = distance by Mario
B = M - 10.65
G = B + 6.9
G = T - 2.75 = 79.25 - 2.75 = 76.5 m
using the 3rd in the second equation :
76.5 = B + 6.9
B = 69.6 m
using this now in the first equation :
69.6 = M - 10.65
M = 80.25 m
step 4 : so, based on the relative results specified in the problem definition, actually Mario won the competition by throwing the ball 80.25 m.
that is a contradiction to the problem definition. something is wrong in the specification.
the discrepancy starts with
Gabe threw 6.9 meters further than Brett but 2.75 meters less than Tyrone.
that means Gabe threw 10.65 - 6.9 = 3.75 meters less than Mario.
so, on one hand, Gabe threw 2.75 meters shorter than the proclaimed winner, but 3.75 meters shorter than another person (Mario). so, Mario threw the ball 3.75 - 2.75 = 1 meter further than the winner ?
therefore, either the distance information about Gabe is wrong, or the info about the winner.