Question

Find four consecutive integers whose sum is 15 less than 5 times the first. ​

Answer 1

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ The four numbers are :

→ 21

→ 22

→ 23

→ 24

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

Given that,

Four consecutive numbers sums to 15 less than 5 times the first.

Step 1 :

$\begin{gathered}{ \textsf{ \textbf{Assuming}}} \begin{cases} \sf{The \: numbers \: are : } \\ \to \sf{(x + 1)}\\ \to \sf{(x + 2)} \\ \to \sf{(x + 3)}\\ \to \sf{(x + 4)}\\ \end{cases} \end{gathered}$

Adds up to :

→ 15 less than 5 times the first

Here, first meant to be the first number i.e., (x + 1)

So,

→ 5(x + 1) - 15

→ 5x + 5 - 15

→ 5x - 10

Step 2 :

✦ Equation forms like this :

• As they adds up to (5x - 10)

$\sf \longrightarrow (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x - 10$

Step 3 :

✦ Solving for x :

$\sf \longrightarrow 4x + 10 = 5x - 10$

$\sf \longrightarrow 10 + 10 = 5x - 4x$

$\sf \longrightarrow x = 20$

Therefore,

➙ The first number is (x + 1) = 21

$\begin{gathered}{ \textsf{ \textbf{Hence}}} \begin{cases} \sf{The \: other \: numbers \: are : } \\ \to \sf{22} \\ \to \sf{23}\\ \to \sf{24}\\ \end{cases} \end{gathered}$

${{\underline{\underline{{\textsf{\textbf{Check point : }}}}}}}$

✦ In accordance to the question it sums to :

• 15 less than 5 times the first.

Or,

→ 5x - 10

→ 5(20) - 10

→ 100 - 10

→ 90

✦ Adding the numbers :

→ 21 + 22 + 23 + 24

→ 90

• Yes they are equal to 90

${{\underline{\underline{{\textsf{\textbf{Hence verified}}}}}}}$ ${\boxed{\green{\checkmark{}}}}$

Answer 2

Answer:

Question

• Find four consecutive integers whose sum is 15 less than 5 times the first.

$\large{\boxed{\bf{Answer}}}$

Given :-

• Four consecutive integers whose sum is 15 less than 5 times the first.

$\bf\underbrace\orange{To Find :-}$

• Four consecutive integers.

$\bf\underbrace\orange{Solution:}$

Let the four consecutive integers be

x, x + 1, x + 2, x + 3.

■ According to statement,

$\bf \:x + x + 1 + x + 2 + x + 3 = 5(x ) - 15$

$\bf\implies \:4x + 6 = 5x - 15$

On transposition, we get

$\bf\implies \:4x - 5x = - 15 - 6$

$\bf\implies \: - x = - 21$

$\bf\implies \:x = 21$

So four consecutive integers are 21, 22, 23, 24

$\bf\underbrace\orange{Verification:}$

$\bf \:Sum \: of \: 4 \: Integers = 21 + 22 + 23 + 24$

$\bf\implies \:90$

$\bf \:15 \: less \: than \: 5 \: times \: the \: first \: = 5 \times 21 - 15 = 90</p><p>$

$\bf \:Hence, verified.$

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