1. When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank?
2. Find consecutive odd integers such that 5 times the sum of the first and the third is 15 more than 5 times the fourth.

1)  There are 72 pennies and 90 nickels

Step-by-step explanation:

x= nickels , y= pennies

0.05x + 0.001y = 5.22

x + y = 162

x= 162-y

use substitution

0.05(162-y)+0.01y = 5.22

multiply 0.05 with the numbers inside the brackets

8.1-0.05y+0.01y=5.22

-0.05y+0.01y=5.22-8.1

-0.04y=-2.88

y=-2.88/-0.04

y=72

162-72=90

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116