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Marina CMI [18]
3 years ago
9

Find 4 consecutive intergers such that the sum of the secound and forth is 34

Mathematics
1 answer:
ankoles [38]3 years ago
4 0
Consecutive integers are 1 aparrt
they are
x,x+1,x+2,x+3

the 2nd and 4th sum is x+1 and x+3
sum is 34
x+1+x+3=34
2x+4=34
minus 4
2x=30
divide 2
x=15

x+1=16
x+2=17
x+3=18

the numbers are 15,16,17,18
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there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three time
hoa [83]

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

0.05x + 0.1y + 0.25z = 3.65

Dimes: 3 times greater than nickels:

This means that:

y = 3x

Quarters: One greater than double the number of nickels:

This means that:

z = 2x + 1

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

0.05x + 0.1y + 0.25z = 3.65

0.05x + 0.1(3x) + 0.25(2x+1) = 3.65

0.05x + 0.3x + 0.5x + 0.25 = 3.65

0.85x = 3.4

x = \frac{3.4}{0.85}

x = 4

y and z:

y = 3x = 3(4) = 12

z = 2x + 1 = 2(4) + 1 = 9

There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at brainly.com/question/17096268

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