Question

: Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation: 0.10d + 0.05n = 22.25

Answer 1

A. (0,445)

D.(118,209)

E.(172,101)

Explanation:

The equation that we have in this problem is:

`0.10d + 0.05n = 22.25`

where

d is the number of dimes

n is the number of nickels

$22.25 is the total amount of money collected by Diego in the jar.

In order to find which pairs of values can be solutions to the equation, we just need to substitute each pair (d,n) into the left term on the equation, and check if the result is 22.25. Let's do it:

A. (0,445)

`0.10\cdot 0 + 0.05\cdot 445 =0+22.25=22.25` --> YES

B. (0.50,435)

`0.10\cdot 0.50 + 0.05\cdot 435 =0.05+21.75=21.80` --> NO

C. (233,21)

`0.10\cdot 233 + 0.05 \cdot 21 =23.3+1.05=24.35` --> NO

D.(118,209)

`0.10\cdot 118 + 0.05\cdot 209 =11.8+10.45=22.25` --> YES

E.(172,101)

`0.10\cdot 172 + 0.05\cdot 101 =17.2+5.05=22.25` --> YES

So the correct pairs are:

A. (0,445)

D.(118,209)

E.(172,101)