Question

Sally has seven times as many dimes as nickels. Their value is \[\$ 3.00\] . How many nickels does she have?

Answer 1

Hint: We need to know the relation between dimes and cents, nickel and cents, dollar with cents to make an easy calculation. Also, we need to know the keyword seven-time, which indicates which operation. This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. The final answer would satisfy the given condition.

Complete step by step solution:
In this question, we have to find how many nickels Sally has.
Before that, we need to find the relation between dime and cent, nickel and cent, dollar and cent.
We know that,
 \[1\] Dime \[ = 10cent\]
 \[1\] \[nickel = 5cent\]
 \[\$ 1 = 100cent\]
Here we know that sally has seven times as many dimes as nickel.
So, let’s take the number of nickel is \[x\] and the number of dimes is \[7x\] . Also, we know what their value is \[\$ 3.00\] .
So, we get the following equation,
 \[7x\] Dimes+ \[x\] nickels= \[\$ 3.00\]
Let’s convert all these units into cents.
We know that \[1\] dime \[ = 10\] cent
So, we have to multiply \[10\] with \[7x\] . So, we get
 \[(7x \times 10)\] Cent \[ + x\] nickel \[ = 3\$ \]
We know that \[1\] nickel \[ = 5\] cent
So, we have to multiply \[5\] with \[x\] . So, we get
 \[(7x \times 10)\] Cent \[ + (x \times 5)\] cent \[ = 3\$ \]
We know that, \[1\$ = 100\] cent
So, we have to multiply \[100\] with \[\$ \] . So, we get
 \[(7x \times 10)\] Cent \[ + (x \times 5)\] cent \[ = (3 \times 100)\] cent
So, finally, we convert all the units in the cent.
Let’s solve the equation,
 \[70x + 5x = 300\]
 \[
  75x = 300 \\
  x = \dfrac{{300}}{{75}} \;
 \]
So, we get
 \[x = 4\]
 \[x = \] Nickel \[ = 4\]
Dimes \[ = 7x = 7 \times 4 = 28\]
So, the final answer is,
Sally has \[4\] nickel and \[28\] dimes.
So, the correct answer is “Sally has \[4\] nickel and \[28\] dimes.”.

Note: Note that one dime is equal to ten cents, one nickel is equal to five cents and one dollar is equal to hundred cents. This type of problems describes the arithmetic operations like addition/ subtraction/ multiplication/ division. Also, note that to solve these types of questions we would take the unknown value as any one of the variables like \[x,y..\] etc , and then solve for the variable and find the remaining value.