I need to solve the problem below but i don't knw how.

Question

A football team scored 30 points in one of its games. It scored a combination of touchdowns (worth 7 points), field goals (worth 3 points), and safeties (worth 2 points). The team scored 3 times as many touchdowns as safeties. The team scored one less field goal than they scored touchdowns. Set up a system of equations in standard form: , that could be used to determine the number of touchdowns, field goals and safeties the team scored.

Answer 1

"a system of equations in standard form" is:

Let t = number of touchdowns

f = number of field goals

s = number of safeties

7t + 3f + 2s = 30 [total score of 30 points'

t - 3s = 0 [three times as many touchdowns as safeties]

t - f = 1 [one less field goal than touchdown]

Answer 2

Let's define some variables for the quantities of touchdowns, t, Field goals, f, and safeties,s and write down all the relationships that we can from the word problem. We need 3 equations for the 3 unknowns for the system of equations to be solvable:

1) Points: 7t + 2s + 3f = 30 Sum of number of times a type of score occurs x points for that score type.

2) t = 3s Given

3) t = f +1 Given

Easiest approach is to put everything in terms of s (t seems obvious, but this avoids fractions in the algebra)

Sub (2) into (1) and (3) into (1), but make it f in terms of s: f = 3s-1

Equation 1 becomes 7(3s) + 2s +3(3s-1) = 30 which doesn't work out. (s = 33/32)

Since the numbers have to be integers, it seems clear that you you can't get 30 pts this way. Perhaps the total score is supposed to be 29 which you can get with 3t, 2f, and 1s.

Anyway, once you have s, you can solve for f and t using equations 3 and 2 respectively.

Answer 3

This is a great exercise on translating words to math, Always begin by defining your variables. We have three unknowns here:

Let t = the number of touchdowns scored

Let f = the number of field goals scored

Let s = the number of safeties scored.

Since we know that touchdowns are worth 7 points, then 7t would be the number of points scored on all touchdowns. Likewise for the other methods of scoring. We also know that the total points scored is 30, so:

7t+3f+2s=30

The other two equations are maybe less intuitive, but just experiment to see that you have them correct,

Three times as many touchdowns as safeties. Re-phrase this as the number of touchdowns (t) is (=) three times the number of safeties (3s), so t = 3s Test this by plugging in some number for t to see if it makes the original statement correct.

Finally, the number of field goals (f) is (=) one less than the number of touchdowns (t-1), So t-1=f

Those are your three equations, which could then be solved by the usual method of elimination or substitution.

Best wishes!

Answer 4

7t + 3f + 2s = 30

t = 3s

f = t - 1

Can you solve the system and answer?