One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?

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One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?

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Answer 1 · 2016-06-16T20:00:11

$n_{1} = 8$ $n_1=8$
$n_{2} = 4$ $n_2=4$

Explanation:

One number is 4 less than $\to n_{1} = ? - 4$ $-> n_1=?-4$
3 times $......................... \to n_{1} = 3 ? - 4$ $" ........................."->n_1=3?-4$
the second number $.......... \to n_{1} = 3 n_{2} - 4$ $color(brown)(".........."->n_1=3n_2-4)$
$\frac{2}{2}$ $color(white)(2/2)$

If 3 more $........................................... \to ? + 3$ $" ..........................................."-> ?+3$
than two times the first number $............ \to 2 n_{1} + 3$ $" ............"->2n_1+3$
is decreased by $................................... \to 2 n_{1} + 3 - ?$ $"..................................."->2n_1+3-?$
2 times the second number $................. \to 2 n_{1} + 3 - 2 n_{2}$ $" ................."->2n_1+3-2n_2$
the result is 11 $..................................... \to 2 n_{1} + 3 - 2 n_{2} = 11$ $color(brown)(" ....................................."->2n_1+3-2n_2=11)$

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$. n_{1} = 3 n_{2} - 4$ $color(white)(.)n_1=3n_2-4$ .....................Equation (1)
$2 n_{1} + 3 - 2 n_{2} = 11$ $2n_1+3-2n_2=11$ ...........Equation (2)

Substitute for $n_{1}$ $n_1$ in equation (2) using equation (1)

$2 n_{1} + 3 - 2 n_{2} = 11 \to 2 (3 n_{2} - 4) + 3 - 2 n_{2} = 11$ $color(brown)(2n_1+3-2n_2=11)" "color(blue)( ->2(3n_2-4)+3-2n_2=11)$

Multiplying out the brackets

$6 n_{2} - 8 + 3 - 2 n_{2} = 11$ $6n_2-8+3-2n_2=11$

$4 n_{2} - 5 = 11$ $4n_2-5=11$

Add 5 to both sides

$4 n_{2} = 16$ $4n_2=16$

Divide both sides by 4

$n_{2} = 4$ $" "color(green)(n_2=4)$
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Substitute $n_{2} = 4$ $n_2=4$ into equation (1)

$n_{1} = 3 (4) - 4$ $n_1=3(4)-4$

$n_{1} = 12 - 4$ $n_1=12-4$

$n_{1} = 8$ $" "color(green)(n_1=8)$
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Check: One number is 4 less than 3 times the second number

$8 = 3 (4) - 4 = 8$ $8=3(4)-4=8$ confirmed!

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One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?

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