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3 years ago

12

Benjamin's age is 6 years less than twice Lucas's age. If Benjamin is 12 years old, how old is Lucas? Choose the answer below th

at is a viable solution to this problem.

2 answers:

sp2606 [1]3 years ago

7 0

Answer: The required age of Luca is 9 years.

Step-by-step explanation: Given that Benjamin's age is 6 years less than twice Lucas's age and Benjamin is 12 years old.

We are to find Luca's age.

Let x and y represents Luca's age and Benjamin's age respectively.

Then, according to the given information, we have

$y=2x-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (ii) in (i), we get

$y=2x-6\\\\\Rightarrow 12=2x-6\\\\\Rightarrow 2x=12+6\\\\\Rightarrow 2x=18\\\\\Rightarrow x=\dfrac{18}{2}\\\\\Rightarrow x=9.$

Thus, the required age of Luca is 9 years.

nikklg [1K]3 years ago

4 0

Answer:

12×2+6 = 30. so Lucas is 30

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Musya8 [376]

Answer:

$8 = 6 + \frac{a}{4} \\ \frac{a}{4 } = 8 - 6 \\ \frac{a}{4} = 2 \\ a = 2 \times 4 \\ a = 8$

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3 years ago

Y ÷ 18 = y ·<br><br> Please answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Elan Coil [88]

Answer:

y/y=18....

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3 0

3 years ago

Ava opens an account with $400. She deposits $200/month for 20 years. The interest rate is 2.15%. How much interest will she hav

artcher [175]

Answer:

d. None of the above

Step-by-step explanation:

We assume the sequence of deposits is ...

month 0: $400

month 1: $200

month 2: $200

...

month 240: $200 . . . . accumulated interest is determined at this point

That is, no interest is earned on the last deposit.

_____

The value of the initial $400 deposit after 20 years at 2.15% interest compounded monthly is ...

$400×(1 +.0215/12)^(12×20) = $400×1.536666 ≈ $614.67

The value of the $200 annuity at the same interest rate is ...

$200((1 +.0215/12)^(12×20) -1)/(.0215/12) = $200×299.534612 ≈ $59,906.92

So, the total account value is ...

$614.67 +59,906.92 = $60521.59

The total amount deposited was ...

$400 +$200×240 = $48,400

The interest earned is the difference between the account value and the total of deposits:

$60,521.59 -48,400 = $12,121.59 . . . . interest earned

This value does not match any numerical answer choice, so we conclude the appropriate answer is ...

None of the above

3 0

3 years ago

Q20-23 with steps pls

just olya [345]

20: Let $x$ be the amount of money. If this amount is shared between 8 people, each person will get x/8 dollars. But there actually are 6 people, so everyone is getting x/6 dollars. We know that this difference results in 30 dollars more, so we have

$\dfrac{x}{6}=\dfrac{x}{8}+30 \iff \dfrac{x}{6}-\dfrac{x}{8}=30$

Rearrange the left hand side as

$\dfrac{4x-3x}{24}=30$

And multiply both sides by 24 to get

$x=720$

21: Let $M$ and $J$ be the number of marbles owned by Mike and Judy, respectively. At the beginning, we have

$M=3J+11$

If they both get 9 more marbles, Mike will have $M+9$ marbles, and Judy will have $J+9$ marbles. So, we have

$M+J+18=93 \iff M+J=75 \iff M=75-J$

Plug this value in the first equation and we have

$75-J=3J+11 \iff 4J=64 \iff J=16$

And we deduce

$M=16\cdot 3 + 11=59$

So, the difference is

$M-J=59-16=43$

22: Let $x,y,z$ be the number of $10, $20 and $50 coupon, respectively. We're given:

$\begin{cases}x=2y+3\\z=\frac{1}{2}y\\x+y+z=38\end{cases}
We can write the third equation by substituting the expressions for x and z:
[tex]x+y+z=(2y+3)+y+\left(\dfrac{1}{2}y\right)=38$

Rearrange as follows:

$(2y+3)+y+\left(\dfrac{1}{2}y\right)=38 \iff \dfrac{7}{2}y=35 \iff 7y=70 \iff y=10$

And now we can deduce the number of the other coupons:

$x=2\cdot 10+3=23,\quad z=\dfrac{1}{2}\cdot 10=5$

So, the total value is

$23\cdot 10+10\cdot 20+5\cdot 50=230+200+100=530$

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$a_1=4\cdot 1+3=7,\quad a_2=4\cdot 2+3=11,\quad a_3=4\cdot 3+3=15$

b) We have

$a_r = 4r+3=71 \iff 4r=68 \iff r=\dfrac{68}{4}=17$

c) 105 is a term of the sequence if and only if there exists an integer k such that

$a_k=4k+3=105 \iff 4k = 102 \iff k=\dfrac{102}{4}=25.5$

So, 105 is not a term of the sequence.

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4 years ago

Solve the formula A=10+ry. solve for y

noname [10]

The given formula $A= 10 + ry$

Solve for y means we have to make y alone

$A= 10 + ry$ \\

Add -10 on both sides, we get

$A - 10 = 10 -10 + ry \\A - 10 = 0 + ryA - 10 = ry$

As there is multiplication sign between r and y so to solve for y, divide both side by r

$\frac{A - 10}{r} = y\\\\y = \frac{A - 10}{r}$

4 0

4 years ago

Read 2 more answers