Faith In The Blood? KJV and Other Bible Translation

As you note, comparing other versions often helps when studying a passage, particularly the difficult passages that the Apostle Paul writes.
The English Standard Version is trustworthy and may, or may not, clarify things for you.
In some cases, a more contemporary, dynamic version like the New Living Translation is helpful but it is not designed to closely follow the Greek structure.

Romans 3:24–25 (ESV): …Christ Jesus, (25) whom God put forward as a propitiation by his blood, to be received by faith….

(Romans 3:25 (NLT) For God sent Jesus to take the punishment for our sins and to satisfy God’s anger against us. We are made right with God when we believe that Jesus shed his blood, sacrificing his life for us. God was being entirely fair and just when he did not punish those who sinned in former times.

Rob

 

Hebrews 9:22, And almost all things are by the law purged with blood; and without shedding of blood is no remission.

 

The NKJV (New King James Version) says:

“whom God set forth [as] a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed,” (Ro 3:25 NKJV)

 

The phrase utilizes a figure of speech, an idiom,
“the blood” representing the crucifixion and death of our Savior.

I’m reminded of a hymn we sang in the past.

What can wash away my sin?
Nothing but the blood of Jesus.
What can make me whole again?
Nothing but the blood of Jesus.

Refrain:
O precious is the flow
that makes me white as snow;
no other fount I know;
nothing but the blood of Jesus.

For my pardon this I see:
nothing but the blood of Jesus.
For my cleansing this my plea:
nothing but the blood of Jesus. [Refrain]

Nothing can for sin atone:
nothing but the blood of Jesus.
Naught of good that I have done:
nothing but the blood of Jesus. [Refrain]

This is all my hope and peace:
nothing but the blood of Jesus.
This is all my righteousness:
nothing but the blood of Jesus. [Refrain]​

*************

Romans 3:25 (NA28)
ὃν προέθετο ὁ θεὸς ἱλαστή
ριον διὰ [τῆς] πίστεως ἐν τῷ
αὐτοῦ αἵματι εἰς ἔνδειξιν
τῆς δικαιοσύνης αὐτοῦ διὰ
τὴν πάρεσιν τῶν προγε
γονότων ἁμαρτημάτων


διὰ - through KJV, NASB, NET, NIV, NRSV,
- - - - by CEV, ESV,

πίστεως - faith (almost all versions)

ἐν - ‘in’ [CEV, GW, KJV, NASB, NCV, NIV],
- - -- ‘by’ [NET, NRSV, NKJV],
αἷμα - ‘blood’ (KJV, NET, NIV, NLT, NRSV, TEV],

The phrase is translated as ‘his death’ [REB], "shed his blood, sacrificing his life for us" (NLT), "by his blood he should become the means by which people’s sins are forgiven" (Good News),

The NET Bible offers and interesting translation of the idiom:

(NET 2nd ed.)
God publicly displayed him at his death as the mercy seat accessible through faith. This was to demonstrate his righteousness, because God in his forbearance had passed over the sins previously committed.​

Rob