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Hunter-Best [27]
3 years ago
13

Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and

will save $25 each month. The second runner has $50 in savings and will save $60 each month.Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
Mathematics
2 answers:
ValentinkaMS [17]3 years ago
6 0

Answer: Our required equation would be

157+25m=50+60m

Step-by-step explanation:

Since we have given that

Amount the first runner has in savings = $112

Amount the first runner received a gift from a friend = $45

Amount the first runner saved each month = $25

Let the number of months be 'm'.

So, Total amount in the first runner account is given by

\$112+\$45+25m\\\\=157+25m

Similarly,

Amount the second runner has in savings = $50

Amount the second runner saved each month = $60

so, the total amount in the second runner account is given by

50+60m

According to question, Both the accounts have same amount of money.

So, it becomes,

157+25m=50+60m\\\\157-50=60m-25m\\\\107=35m\\\\\dfrac{107}{35}=m\\\\m=3.05\approx 3\ months

Hence, our required equation would be

157+25m=50+60m

Tcecarenko [31]3 years ago
4 0
Hope this helps but I think the answer could be : 157+25m=50+60m
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Show work and explain with formulas:
Marina86 [1]

17 Answer:  205

<u>Step-by-step explanation:</u>

\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n

\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}

18 Answer:  1968

<u>Step-by-step explanation:</u>

a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88

\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}

19 Answer:  -116

<u>Step-by-step explanation:</u>

\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}

6 0
3 years ago
I rlly rlly need the answer ASAP
Natalija [7]

Answer:

your answer is c

Step-by-step explanation:

In the fraction Jonah made split his table into 10 parts to show 3/5 and to get the 10 parts he multiplied 5 by 2 to get 10 and you have to do the same to the 3 so 3 multiplied by 2 is 6

3 0
3 years ago
Please answer do not answer if u don't know the answer
Hitman42 [59]

Answer :x=3 y=7 (3,7)

Step-by-step explanation: I took algebra last year and I answered your question earlier.

4 0
3 years ago
A horticulturist wants to improve the soil quality in a garden by adding 120 pounds of nitrogen and 54 pounds of potassium. A pa
eimsori [14]

x and y are the packs of organic and inorganic fertilizer, respectively.

pounds of nitrogen added = 2x + 6y = 120

pounds of potassium added = 3x + 2y = 54

eliminate the y terms. subtract the first equation from 3 times the second equation.

9x + 6y = 162

-2x - 6y = -120

------------------

7x = 42

x = 6

y = 18

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3 years ago
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GrogVix [38]

Answer:

I don´t remember how to do this sorry

Step-by-step explanation:

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