# math

posted by .

Mia is approaching her goal of 119 points for the video game. She wants to put her initials on the computerized list of Top Ten Point Scorers forr the game, She moves Freddie the frog all over the terminal screen and at last she does it. Freddie the Frog eats a total of 22 critters: worm ( worth 6 points each), bugs ( worth 7 points each). and butterfies ( worth 4 points each). if Mia earned the total of 119 points, how many critters of each type did her frog eat?

• math -

w=worms, g=bugs, f=butterflies

count critters: w+g+f = 22
count points: 6w+7g+4f = 119

6w+7g+4f = 4(w+g+f) + 2w + 5f
4(22) + 2w + 5g = 119
2w + 5g = 119-88 = 31

Now, we don't know how many w,g we have, but since 2w is even, that means 5g must be odd, which means that g must be odd.

Take a look at possibilities:

g=1: 2w+5 = 31 ==> w=13 f=8
g=3: 2w+15 = 31 ==> w=8 f=11
g=5: 2w+25 = 31 ==> w=3 f=14

Those are the only possible solutions

• math -

Good solution, Steve, but w+b+f=6+7+4=17.
worms (w) - 6
bugs (b) - 7
butterflies (f)- 4

critters: w+b+f=22

points: 6w+7b+4f=119 (the only way to get an odd number is if b is odd)

points from having one of each of the critters: w+b+f -> 6+7+4=17

so, using the points now:
6w+7b+4f=119
Break apart each set of critters into 4+something:

4w+2w+4b+3b+4f=119
Which means 4w+4b+4f+2w+3b=119

But 4w+4b+4f=4(w+b+f)=4(22) – (this is when she has equal amounts of each critter)

So 4(22)+2w+3b=119
2w+3b=119-88=31

2w+3b=31 (which can only be odd if b is odd, so try values for b)
b=1, 2w+3=31, w=14, f=7 (f=22-1-14) -> w=14, b=1, f=7
b=3, 2w+9=31, w=11, f=8 -> w=11, b=3, f=8
b=5, 2w+15=31, w=8, f=9 -> w=8, b=5, f=9
b=7, 2w+21=31, w=5, f=10 -> w=5, b=7, f=10
b=9, 2w+27=31, w=2, f=11 -> w=2, b=9, f=11

If b is larger than 9, 2w+3b will be larger than 31, so no more solutions.

• math -

Nic, your solution is a bit confusing as it contains 6+4+7. instead, try this:
worms-w-9
bugs-b-10
butterflies-f-3
11b+1w
or...
11b+3f

11b=110
1w=9
3f=9

110+9=119

SOLVED!

## Similar Questions

1. ### algebra

amys bowling score in her 3rd game was 10 less that her score in her first game and 5 more than her second game. The total points of all 3 games were 275. What is the highest number of points she could have scored in her first game?
2. ### Physics

3. It’s fourth down in the big football game, and the game is tied with 2 seconds to go! You are called on to win the game with the biggest field goal of your life, from 36 meters. The crowd holds its collective breath as the ball …
3. ### math

- Three hockey teams, the Crabs, the Eels, and the Seals, played each other once with no shutouts ( every team scored at least 1 goal in each game). A team gets 10 points for a win, 5 point for a tie and one point for each goal scored. …
4. ### math

- Three hockey teams, the Crabs, the Eels, and the Seals, played each other once with no shutouts ( every team scored at least 1 goal in each game). A team gets 10 points for a win, 5 point for a tie and one point for each goal scored. …

In basketball you score 2 points for a field goal and 1 point for a free throw. Suppose that you have scored at least 3 points in every game this season, and have a season high score of 15 points in one game. How many field goals and …
6. ### math

How would I write 2 inequalities that describe in basketball that 2 points = field goal and 1 point = free throw and I have scored at least 3 points in every game this season and 15 points for the most points in one game?
7. ### math

In a football game, a touchdown with an extra point is worth 7 points and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns with extra points and field goals. A: Which of the scores …
8. ### Math

The original price of a video game is \$32. Prince buys the video game when it is on sale for 30% off the regular price. If the sales tax is 10%, how much will Prince pay for the video game?
9. ### algebra 1

In a basketball game you score 2 points for a field goal and 1 point for a free throw. Suppose that you have scored at least 5 points a game and have a season high of 12 points a game. How many field goals and free throws could you …
10. ### math

In a football game, a touchdown with an extra point is worth 7 points and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns please help!!!!

More Similar Questions