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3 years ago

The difference of two numbers is 18 and their sum is 90 find the two numbers

Mathematics

1 answer:

Mariulka [41]3 years ago

8 0

Answer 36 and 54

x and x+18 are the numbers

x+(x+18)=90

2x+18=90

2x=72

x=36

x+18=54

36 and 54 are the numbers

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The amount each took home was 20 unit currency.

Step-by-step explanation:

We are given that Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140 apples, went to market and sold all their apples at the same price, and each received the same sum of money.

Formula : $a \times n + (n - 1)$ , $(a + b)\cdot n + (n - 2)$ , $(a + 2 \cdot b) \cdot n + (n - 3)$ , $(a + 3 \cdot b) \cdot n + (n - 4)$ , $(a + 4 \cdot b) \cdot n + (n - 5)$ , $(a + 5 \cdot b) \cdot n + (n - 6)$ , $(a + 6 \cdot b) \cdot n + (n - 7)$

$a \cdot n + (n - 1) = 20$

$(a + b) \cdot n + (n - 2)=40$

$(a + 2 \cdot b) \cdot n + (n - 3) = 60$

$(a + 3 \cdot b) \cdot n + (n - 4) = 80$

$(a + 4 \cdot b) \cdot n + (n - 5) = 100$

$(a + 5 \cdot b) \cdot n + (n - 6) = 120$

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On solving :

n = 7, a = 2, b = 3

So,

$2 \times 7 + 6 = 20$

$5 \times 7 + 5=40$

$8 \times 7 + 4 = 60$

$11 \times 7 + 3 = 80$

$14 \times 7 + 2 = 100$

$17 \times 7 + 1 = 120$

Based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount :

2×1 + 6×3 = 20

5×1 + 5×3=20

8×1 + 4×3 = 20

11×1 + 3×3 = 20

14×1 + 2×3 = 20

17×1 + 1×3 = 20

20×1 = 20

Therefore, the amount each took home was 20 unit currency.

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