Question

Determinați numărul a pentru care
{[(a + 2 x 3) x 4 + 5 x 6] x 7 + 8 x 9} x 10 = 8140.

Pls

Answer 1

((( a + 2 × 3 ) × 4 + 5 × 6 ) × 7 + 8 × 9 ) × 10 = 8140

((( a + 6 ) × 4 + 30 ) × 7 + 72 ) × 10 = 8140

(( 4 × a + 24 + 30 ) × 7 + 72 ) × 10 = 8140

(( 4 × a + 54 ) × 7 + 72 ) × 10 = 8140

(( 28 × a + 378 + 72 ) × 10 = 8140

( 28 × a + 450 ) × 10 = 8140

280 × a + 4500 = 8140

280 × a = 8140 - 4500

280 × a = 3640

a = 3640 : 280

a = 13

Answer 2

Răspuns: a = 13

Explicație pas cu pas:

Metoda mersului invers

{[(a + 2 × 3) × 4 + 5 × 6] × 7 + 8 × 9} × 10 = 8140

{[(a + 6) × 4 + 30] × 7 + 72} × 10 = 8140

[(a + 6) × 4 + 30] × 7 + 72 = 8140 ÷ 10

[(a + 6) × 4 + 30] × 7 + 72 = 814

[(a + 6) × 4 + 30] × 7 = 814 - 72

[(a + 6) × 4 + 30] × 7 = 742

(a + 6) × 4 + 30 = 742 ÷ 7

(a + 6) × 4 + 30 = 106

(a + 6) × 4 = 106 - 30

(a + 6) × 4 = 76

a + 6 = 76 ÷ 4

a + 6 = 19

a = 19 - 6

a = 13 ➡ numărul, aflat prin metoda mersului invers

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Verificare: {[(13 + 2 × 3) × 4 + 5 × 6] × 7 + 8 × 9} × 10 = 8140

{[(13 + 6) × 4 + 30] × 7 + 72} × 10 = 8140

[(19 × 4 + 30) × 7 + 72] × 10 = 8140

[(76 + 30) × 7 + 72] × 10 = 8140

(106 × 7 + 72) × 10 = 8140

(742 + 72) × 10 = 8140

814 × 10 = 8140

8140 = 8140 ✔