Your family likes to go to baseball games. at one game your family bought 5 soft drinks and 5 hot dogs for $22.25. at the next game your family attended they bought 4 soft drinks and 3 hot dogs for $14.50. what is the cost of one soft drink and one hot dog? let s = the cost of one soft drink let h = the cost of one hot dog a. write a system of equations modeling the situation described above. b. solve the system for the cost of one soft drink + one hot dog. (you will have to add your solutions together for this one.)

Step-by-step explanation:

The first equation is

  5s  + 5h  =  22.25

The second equation is

 4s  +  3h  =  14.50

If we solve this system by elimination, we can multiply the first equation by -4 and the second one by +5 to first eliminate the s terms.  After multipying each equation through by its scalar multiple, we have a new set of equations:

 -20s  -  20h  =  -89

  20s  +  15h  =  72.50

Now the s terms subtract each other away, leaving us with

 -5h  =  -16.5 so

 h  =  3.30

Now we can take that h value and sub it back into one of the original equations and find s:

5s + 5(3.3) = 22.25 and

5s + 16.5 = 22.25 and

5s = 5.75 so

s = 1.15

For one drink and one hot dog you will spend 1.15 + 3.30 = $4.45

  $4.45

Step-by-step explanation:

(a) The situation can be modeled by the system of equations ...

  5s + 5h = 22.25

  4s +3h = 14.50

__

(b) You are asked to find the value of s+h. Divide the first equation by 5 and you have that result:

  s + h = 4.45

The cost of one soft drink and one hot dog is $4.45.

Comment on the problem and solution

The first step in solving the problem is to understand how what you're given relates to what you're asked to find.

Here, you're given a value for 5 drinks and 5 hot dogs, and you're asked to find the value of 1 drink and 1 hot dog. You do not need to know the individual costs of the items. The cost of 1 combination is 1/5 the cost of 5 of them.

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!