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stira [4]
4 years ago
6

All 231 students in the math club went on a field trip in 15 vehicles. Some students rode in vans which holds 7 students each an

d some students ride in buses which holds 25 students each. How many vans and buses were used?
Mathematics
1 answer:
Rina8888 [55]4 years ago
7 0

They used 8 vans and 7 buses

Step-by-step explanation:

The given is:

  • All 231 students in the math club went on a field trip in 15 vehicles
  • Some students rode in vans which holds 7 students each and some students ride in buses which holds 25 students each

We need to find how many vans and buses were used

Assume that the number of vans is x and the number of buses is y

∵ There were x vans in the trip

∵ There were y buses in the trip

∵ They went in 15 vehicles

- Add x and y and equate the sum by 15

∴ x + y = 15 ⇒ (1)

∵ Each van holds 7 students

∵ Each bus holds 25 students

∵ 231 students went to the trip

- Multiply x by 7 and y by 25, then add the products and equate

  the sum by 231

∴ 7x + 25y = 231 ⇒ (2)

Now we have a system of equation to solve it

Multiply equation (1) by -7 to eliminate x

∵ -7x - 7y = -105 ⇒ (3)

- Add equations (2) and (3)

∴ 18y = 126

- Divide both sides by 18

∴ y = 7

- Substitute the value of y in equation (1) to find x

∵ x + 7 = 15

- Subtract 7 from both sides

∴ x = 8

They used 8 vans and 7 buses

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

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Answer:

1.67 m/s

Step-by-step explanation:

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<u>Jorge walks in total:</u>

  • 750 m + 250 m = 1000 m

<u>I takes him:</u>

  • 600 seconds

<u>His speed is:</u>

  • 1000 m /600 s ≈ 1.67 m/s
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6 0
3 years ago
Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest
Nostrana [21]

The amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

<h3>What is monthly payment?</h3>

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

It can be calculated with the following formula.

M=P\left (\dfrac{r}{1-(1+r)^{-nt}}\right)

Here, (<em>P</em>) is the principal amount, (<em>r</em>) is the interest rate and (<em>t</em>) is time.

Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate.

The table below shows the information about the two credit cards Brandon currently uses.    

  • Cards                Amount              APR             Monthly Payment
  • Card a               $1,463.82              13%                 $24.60
  • Card b               $1,157.98               17%                 $22.14

               

Interest rate for the card a is,

r=\dfrac{13}{12\times100}=0.01083

The time period is 8 years and there are 12 months in one year. Thus, the monthly payment of card A will be,

M=1157.98\left (\dfrac{0.01083}{1-(1+0.01083)^{-12(8)}}\right)\\M=19.47

In the 8 years, there is total 96 monthly payments. Thus, the total payment by card A is,

P_a=19.47\times96=1869.12

For the card B the monthly payment is $22.14. Thus the total payment by card B is,

P_b=22.14\times96=2125.44

The difference in the payment is,

d=2125.44-1869.12\\d=256.12

Hence, the amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

Learn more about the monthly payment here;

brainly.com/question/2151013

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3 years ago
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